Moduli Of Double Epw Sextics

Author : Kieran G. O'Grady
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 41,6 Mb
Release : 2016-03-10
Category : Equations, Sextic
ISBN : 9781470416966

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Moduli of Double EPW-Sextics by Kieran G. O'Grady Pdf

The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of ⋀3C6 modulo the natural action of SL6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3[2] polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.

Author : Jan Arthur Christophersen,Kristian Ranestad
Publisher : Springer
Page : 326 pages
File Size : 55,9 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783319948812

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Geometry of Moduli by Jan Arthur Christophersen,Kristian Ranestad Pdf

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Author : Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil
Publisher : American Mathematical Soc.
Page : 614 pages
File Size : 44,8 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 9780821889831

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A Celebration of Algebraic Geometry by Brendan Hassett,James McKernan,Jason Starr,Ravi Vakil Pdf

This volume resulted from the conference A Celebration of Algebraic Geometry, which was held at Harvard University from August 25-28, 2011, in honor of Joe Harris' 60th birthday. Harris is famous around the world for his lively textbooks and enthusiastic teaching, as well as for his seminal research contributions. The articles are written in this spirit: clear, original, engaging, enlivened by examples, and accessible to young mathematicians. The articles in this volume focus on the moduli space of curves and more general varieties, commutative algebra, invariant theory, enumerative geometry both classical and modern, rationally connected and Fano varieties, Hodge theory and abelian varieties, and Calabi-Yau and hyperkähler manifolds. Taken together, they present a comprehensive view of the long frontier of current knowledge in algebraic geometry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Author : Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 49,5 Mb
Release : 2013-05-17
Category : Mathematics
ISBN : 9781461464822

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Birational Geometry, Rational Curves, and Arithmetic by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Pdf

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Author : Anonim
Publisher : Unknown
Page : 630 pages
File Size : 44,6 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015072629531

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Pure and Applied Mathematics Quarterly by Anonim Pdf

Author : Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini
Publisher : Springer Nature
Page : 200 pages
File Size : 54,6 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030371142

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Birational Geometry and Moduli Spaces by Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini Pdf

This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

Author : Brayton Gray
Publisher : American Mathematical Soc.
Page : 111 pages
File Size : 44,5 Mb
Release : 2017-02-20
Category : Abelian groups
ISBN : 9781470423087

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Abelian Properties of Anick Spaces by Brayton Gray Pdf

Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. This work describes their -space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).

Author : Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 40,6 Mb
Release : 2016-10-05
Category : 1-factorization
ISBN : 9781470420253

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Proof of the 1-Factorization and Hamilton Decomposition Conjectures by Béla Csaba,Daniela Kühn,Allan Lo,Deryk Osthus,Andrew Treglown Pdf

In this paper the authors prove the following results (via a unified approach) for all sufficiently large n: (i) [1-factorization conjecture] Suppose that n is even and D≥2⌈n/4⌉−1. Then every D-regular graph G on n vertices has a decomposition into perfect matchings. Equivalently, χ′(G)=D. (ii) [Hamilton decomposition conjecture] Suppose that D≥⌊n/2⌋. Then every D-regular graph G on n vertices has a decomposition into Hamilton cycles and at most one perfect matching. (iii) [Optimal packings of Hamilton cycles] Suppose that G is a graph on n vertices with minimum degree δ≥n/2. Then G contains at least regeven(n,δ)/2≥(n−2)/8 edge-disjoint Hamilton cycles. Here regeven(n,δ) denotes the degree of the largest even-regular spanning subgraph one can guarantee in a graph on n vertices with minimum degree δ. (i) was first explicitly stated by Chetwynd and Hilton. (ii) and the special case δ=⌈n/2⌉ of (iii) answer questions of Nash-Williams from 1970. All of the above bounds are best possible.

Author : Xin-Rong Dai,Qiyu Sun
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 45,6 Mb
Release : 2016-10-05
Category : Gabor frames
ISBN : 9781470420154

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The $abc$-Problem for Gabor Systems by Xin-Rong Dai,Qiyu Sun Pdf

A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.

Author : Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 44,6 Mb
Release : 2017-04-25
Category : Operator algebras
ISBN : 9781470423094

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Semicrossed Products of Operator Algebras by Semigroups by Kenneth R. Davidson,Adam Fuller,Evgenios T. A. Kakariadis Pdf

The authors examine the semicrossed products of a semigroup action by -endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Author : Yves Le Jan,Michael B. Marcus,Jay Rosen
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 50,8 Mb
Release : 2017-04-25
Category : Gaussian processes
ISBN : 9781470436957

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Intersection Local Times, Loop Soups and Permanental Wick Powers by Yves Le Jan,Michael B. Marcus,Jay Rosen Pdf

Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

Author : Steve Hofmann,Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 45,7 Mb
Release : 2017-01-18
Category : Function spaces
ISBN : 9781470422608

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$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets by Steve Hofmann,Dorina Mitrea,Marius Mitrea Pdf

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces. The local theorem is then used to establish an inductive scheme in which square function estimates on so-called big pieces of an Ahlfors-David regular set are proved to be sufficient for square function estimates to hold on the entire set. Extrapolation results for and Hardy space versions of these estimates are also established. Moreover, the authors prove square function estimates for integral operators associated with variable coefficient kernels, including the Schwartz kernels of pseudodifferential operators acting between vector bundles on subdomains with uniformly rectifiable boundaries on manifolds.

Author : Isabel Averill,King-Yeung Lam,Yuan Lou
Publisher : American Mathematical Soc.
Page : 1060 pages
File Size : 53,6 Mb
Release : 2017-01-18
Category : Bifurcation theory
ISBN : 9781470422028

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The Role of Advection in a Two-Species Competition Model: A Bifurcation Approach by Isabel Averill,King-Yeung Lam,Yuan Lou Pdf

The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by using the advection rate as the bifurcation parameter. This approach enables the authors to capture the change of dynamics from weak advection to strong advection. The authors determine three different types of bifurcation diagrams, depending on the difference of diffusion rates. Some exact multiplicity results about bifurcation points are also presented. The authors' results can unify some previous work and, as a case study about the role of advection, also contribute to the understanding of intermediate (relative to diffusion) advection in reaction-diffusion models.

Author : Reiner Hermann:
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 49,9 Mb
Release : 2016-09-06
Category : Associative rings
ISBN : 9781470419950

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Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology by Reiner Hermann: Pdf

In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Author : F. Dahmani,V. Guirardel,D. Osin
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 46,7 Mb
Release : 2017-01-18
Category : Hyperbolic groups
ISBN : 9781470421946

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Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces by F. Dahmani,V. Guirardel,D. Osin Pdf

he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.