Exceptional Vector Bundles Tilting Sheaves And Tilting Complexes For Weighted Projective Lines

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Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines

Hagen Meltzer,Richard D. Canary,Darryl McCullough
Exceptional Vector Bundles Tilting Sheaves and Tilting Complexes for Weighted Projective Lines Book PDF

Author : Hagen Meltzer,Richard D. Canary,Darryl McCullough
Publisher : American Mathematical Soc.
Page : 139 pages
File Size : 47,7 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835197

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Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines by Hagen Meltzer,Richard D. Canary,Darryl McCullough Pdf

This work deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves. We study exceptional vector bundles on weighted projective lines and show in particular that the braid group acts transitively on the set of complete exceptional sequences of such bundles. We further investigate tilting sheaves on weighted projective lines and determine the Auslander-Reiten components of modules over their endomorphism rings. Finally we study tilting complexes in the derived category and present detailed classification results in the case of weighted projective lines of hyperelliptic type.

Noncommutative Curves of Genus Zero

Dirk Kussin
Noncommutative Curves of Genus Zero Book PDF

Author : Dirk Kussin
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 46,7 Mb
Release : 2009-08-07
Category : Mathematics
ISBN : 9780821844007

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Noncommutative Curves of Genus Zero by Dirk Kussin Pdf

In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.

Representation Theory of Geigle-Lenzing Complete Intersections

Martin Herschend,Osamu Iyama,Hiroyuki Minamoto,Steffen Oppermann
Representation Theory of Geigle Lenzing Complete Intersections Book PDF

Author : Martin Herschend,Osamu Iyama,Hiroyuki Minamoto,Steffen Oppermann
Publisher : American Mathematical Society
Page : 156 pages
File Size : 51,8 Mb
Release : 2023-05-23
Category : Mathematics
ISBN : 9781470456313

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Representation Theory of Geigle-Lenzing Complete Intersections by Martin Herschend,Osamu Iyama,Hiroyuki Minamoto,Steffen Oppermann Pdf

View the abstract. https://www.ams.org/bookstore/pspdf/memo-285-1412-abstract.pdf?

Representations of Algebras and Related Topics

Andrzej Skowroński,Kunio Yamagata
Representations of Algebras and Related Topics Book PDF

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 50,9 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

Infinite Dimensional Complex Symplectic Spaces

William Norrie Everitt,Lawrence Markus,Johannes Huebschmann
Infinite Dimensional Complex Symplectic Spaces Book PDF

Author : William Norrie Everitt,Lawrence Markus,Johannes Huebschmann
Publisher : American Mathematical Soc.
Page : 76 pages
File Size : 47,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835456

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Infinite Dimensional Complex Symplectic Spaces by William Norrie Everitt,Lawrence Markus,Johannes Huebschmann Pdf

Complex symplectic spaces, defined earlier by the authors in their ""AMS Monograph"", are non-trivial generalizations of the real symplectic spaces of classical analytical dynamics. These spaces can also be viewed as non-degenerate indefinite inner product spaces, although the authors here follow the lesser known exposition within complex symplectic algebra and geometry, as is appropriate for their prior development of boundary value theory. In the case of finite dimensional complex symplectic spaces it was shown that the corresponding symplectic algebra is important for the description and classification of all self-adjoint boundary value problems for (linear) ordinary differential equations on a real interval.In later ""AMS Memoirs"" infinite dimensional complex symplectic spaces were introduced for the analysis of multi-interval systems and elliptic partial differential operators. In this current Memoir the authors present a self-contained, systematic investigation of general complex symplectic spaces, and their Lagrangian subspaces, regardless of the finite or infinite dimensionality - starting with axiomatic definitions and leading towards general Glazman-Krein-Naimark (GKN) theorems.In particular, the appropriate relevant topologies on such a symplectic space $\mathsf{S}$ are compared and contrasted, demonstrating that $\mathsf{S}$ is a locally convex linear topological space in terms of the symplectic weak topology. Also the symplectic invariants are defined (as cardinal numbers) characterizing $\mathsf{S}$, in terms of suitable Hilbert structures on $\mathsf{S}$. The penultimate section is devoted to a review of the applications of symplectic algebra to the motivating of boundary value problems for ordinary and partial differential operators. The final section, the Aftermath, is a review and summary of the relevant literature on the theory and application of complex symplectic spaces. The Memoir is completed by symbol and subject indexes.

Integrable Hamiltonian Systems on Complex Lie Groups

Velimir Jurdjevic
Integrable Hamiltonian Systems on Complex Lie Groups Book PDF

Author : Velimir Jurdjevic
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 46,7 Mb
Release : 2005
Category : Hamiltonian systems
ISBN : 9780821837641

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Integrable Hamiltonian Systems on Complex Lie Groups by Velimir Jurdjevic Pdf

Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and the symplectic geometry of the Lie algebra $\mathfrak{g}, $ of $G$

The Complex Monge-Ampere Equation and Pluripotential Theory

Sławomir Kołodziej
The Complex Monge Ampere Equation and Pluripotential Theory Book PDF

Author : Sławomir Kołodziej
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 52,7 Mb
Release : 2005
Category : Monge-Ampère equations
ISBN : 9780821837634

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The Complex Monge-Ampere Equation and Pluripotential Theory by Sławomir Kołodziej Pdf

We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.

Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis

J. T. Cox,Jeff Groah,Donald Andrew Dawson,Blake Temple,Andreas Greven
Mutually Catalytic Super Branching Random Walks Large Finite Systems and Renormalization Analysis Book PDF

Author : J. T. Cox,Jeff Groah,Donald Andrew Dawson,Blake Temple,Andreas Greven
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 54,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835425

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Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis by J. T. Cox,Jeff Groah,Donald Andrew Dawson,Blake Temple,Andreas Greven Pdf

We study features of the longtime behavior and the spatial continuum limit for the diffusion limit of the following particle model. Consider populations consisting of two types of particles located on sites labeled by a countable group. The populations of each of the types evolve as follows: each particle performs a random walk and dies or splits in two with probability $\frac{1} {2}$ and the branching rates of a particle of each type at a site $x$ at time $t$ is proportional to the size of the population at $x$ at time $t$ of the other type. The diffusion limit of ''small mass, large number of initial particles'' is a pair of two coupled countable collections of interacting diffusions, the mutually catalytic super branching random walk.Consider now increasing sequences of finite subsets of sites and define the corresponding finite versions of the process. We study the evolution of these large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. A dichotomy is known between transient and recurrent symmetrized migrations for the infinite system, namely, between convergence to equilibria allowing for coexistence in the first case and concentration on monotype configurations in the second case.Correspondingly we show in the recurrent case both large finite and infinite systems behave similar in all time scales, in the transient case we see for small time scales a behavior resembling the one of the infinite system, whereas for large time scales the system behaves as in the finite case with fixed size and finally in intermediate scales interesting behavior is exhibited, the system diffuses through the equilibria of the infinite system which are indexed by the pair of intensities and this diffusion process can be described as mutually catalytic diffusion on $(\R^ )^2$. At the same time, the above finite system asymptotics can be applied to mean-field systems of $N$ exchangeable mutually catalytic diffusions. This is the building block for a renormalization analysis of the spatially infinite hierarchical model and leads to an association of this system with the so-called interaction chain, which reflects the behavior of the process on large space-time scales.Similarly we introduce the concept of a continuum limit in the hierarchical mean field limit and show that this limit always exists and that the small-scale properties are described by another Markov chain called small scale characteristics. Both chains are analyzed in detail and exhibit the following interesting effects. The small scale properties of the continuum limit exhibit the dichotomy, overlap or segregation of densities of the two populations, as a function of the underlying random walk kernel. A corresponding concept to study hot spots is presented. Next we look in the transient regime for global equilibria and their equilibrium fluctuations and in the recurrent regime on the formation of monotype regions.For particular migration kernels in the recurrent regime we exhibit diffusive clustering, which means that the sizes (suitable defined) of monotype regions have a random order of magnitude as time proceeds and its distribution is explicitly identifiable. On the other hand in the regime of very large clusters we identify the deterministic order of magnitude of monotype regions and determine the law of the random size. These two regimes occur for different migration kernels than for the cases of ordinary branching or Fisher-Wright diffusion. Finally we find a third regime of very rapid deterministic spatial cluster growth which is not present in other models just mentioned. A further consequence of the analysis is that mutually catalytic branching has a fixed point property under renormalization and gives a natural example different from the trivial case of multitype models consisting of two independent versions of the fixed points for the one type case.

Locally Finite Root Systems

Ottmar Loos,Erhard Neher
Locally Finite Root Systems Book PDF

Author : Ottmar Loos,Erhard Neher
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 55,8 Mb
Release : 2004
Category : Lie superalgebras
ISBN : 9780821835463

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Locally Finite Root Systems by Ottmar Loos,Erhard Neher Pdf

We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: the intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.

Quasi-Ordinary Power Series and Their Zeta Functions

Enrique Artal-Bartolo
Quasi Ordinary Power Series and Their Zeta Functions Book PDF

Author : Enrique Artal-Bartolo
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 40,8 Mb
Release : 2005-10-05
Category : Functions, Zeta
ISBN : 0821865633

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Quasi-Ordinary Power Series and Their Zeta Functions by Enrique Artal-Bartolo Pdf

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h,T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h,T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action on the complex $R\psi_h$ of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.

A Random Tiling Model for Two Dimensional Electrostatics

Mihai Ciucu
A Random Tiling Model for Two Dimensional Electrostatics Book PDF

Author : Mihai Ciucu
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 45,5 Mb
Release : 2005
Category : Electrostatics
ISBN : 9780821837948

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A Random Tiling Model for Two Dimensional Electrostatics by Mihai Ciucu Pdf

Studies the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. This book analyzes the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges.

Lax-Phillips Scattering and Conservative Linear Systems: A Cuntz-Algebra Multidimensional Setting

Joseph A. Ball,Victor Vinnikov
Lax Phillips Scattering and Conservative Linear Systems A Cuntz Algebra Multidimensional Setting Book PDF

Author : Joseph A. Ball,Victor Vinnikov
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 46,6 Mb
Release : 2005
Category : Algèbres d'opérateurs
ISBN : 9780821837689

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Lax-Phillips Scattering and Conservative Linear Systems: A Cuntz-Algebra Multidimensional Setting by Joseph A. Ball,Victor Vinnikov Pdf

The evolution operator for the Lax-Phillips scattering system is an isometric representation of the Cuntz algebra, while the nonnegative time axis for the conservative, linear system is the free semigroup on $d$ letters. This title presents a multivariable setting for Lax-Phillips scattering and for conservative, discrete-time, linear systems.

Higher Complex Torsion and the Framing Principle

Kiyoshi Igusa
Higher Complex Torsion and the Framing Principle Book PDF

Author : Kiyoshi Igusa
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 47,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837733

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Higher Complex Torsion and the Framing Principle by Kiyoshi Igusa Pdf

We prove that higher Franz-Reidemeister (FR) torsion satisfies the transfer property and a formula known as the 'Framing Principle' in full generality. We use these properties to compute the higher FR-torsion for all smooth bundles with oriented closed even dimensional manifold fibers. We also show that the higher complex torsion invariants of bundles with closed almost complex fibers are multiples of generalized Miller-Morita-Mumford classes.

A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring

Ehud Friedgut,Vojtěch Rödl,Andrzej Ruciński,Prasad Tetali
A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring Book PDF

Author : Ehud Friedgut,Vojtěch Rödl,Andrzej Ruciński,Prasad Tetali
Publisher : American Mathematical Soc.
Page : 66 pages
File Size : 40,6 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821838259

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A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring by Ehud Friedgut,Vojtěch Rödl,Andrzej Ruciński,Prasad Tetali Pdf

Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper we establish a sharp threshold for random graphs with this property. Let $G(n,p)$ be the random graph on $n$ vertices with edge probability $p$. We prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\left[G(n,(1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right] \rightarrow 0$ and $Pr \left[G(n,(1+\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right] \rightarrow 1. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting.

Kahler Spaces, Nilpotent Orbits, and Singular Reduction

Johannes Huebschmann
Kahler Spaces Nilpotent Orbits and Singular Reduction Book PDF

Author : Johannes Huebschmann
Publisher : American Mathematical Soc.
Page : 96 pages
File Size : 47,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835722

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Kahler Spaces, Nilpotent Orbits, and Singular Reduction by Johannes Huebschmann Pdf

For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: the closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS', and certain pre-homogeneous spaces appear as different incarnations of the same structure.The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups.Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.