Newton Polyhedra Without Coordinates Newton Polyhedra Of Ideals

Author : Boris Youssin
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 41,8 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821824955

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Newton Polyhedra without Coordinates/Newton Polyhedra of Ideals by Boris Youssin Pdf

This book creates a commutative algebra background for explicit and canonical resolution of singularities of algebraic varieties. The author's construction provides a coordinate-free definition of some Newton polyhedra related to a germ of functions or an ideal. In addition, the construction is significant as a step toward an explicit and canonical resolution of singularities in characteristic zero. The book is intended for researchers in algebraic geometry and commutative algebra.

Author : Margherita Galbiati,Alberto Tognoli
Publisher : Springer
Page : 371 pages
File Size : 51,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540469520

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Real Analytic and Algebraic Geometry by Margherita Galbiati,Alberto Tognoli Pdf

Author : Isroil A. Ikromov,Detlef Müller
Publisher : Princeton University Press
Page : 268 pages
File Size : 52,6 Mb
Release : 2016-05-24
Category : Mathematics
ISBN : 9780691170558

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Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194) by Isroil A. Ikromov,Detlef Müller Pdf

This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface. Isroil Ikromov and Detlef Müller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Müller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger. Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.

Author : Michael Schneider,Yum-Tong Siu
Publisher : Cambridge University Press
Page : 582 pages
File Size : 55,5 Mb
Release : 1999
Category : Mathematics
ISBN : 0521770866

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Several Complex Variables by Michael Schneider,Yum-Tong Siu Pdf

Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.

Author : T. Mora,C. Traverso
Publisher : Springer Science & Business Media
Page : 504 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204411

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Effective Methods in Algebraic Geometry by T. Mora,C. Traverso Pdf

The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary ing; an average meaning is "Applied Algebra and Error Correcting Codes").

Author : Brian D. Boe,David H. Collingwood
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 43,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825471

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Enright-Shelton Theory and Vogan's Problem for Generalized Principal Series by Brian D. Boe,David H. Collingwood Pdf

This book investigates the composition series of generalized principal series representations induced from a maximal cuspidal parabolic subgroup of a real reductive Lie group. Boe and Collingwood study when such representations are multiplicity-free (Vogan's Problem #3) and the problem of describing their composition factors in closed form. The results obtained are strikingly similar to those of Enright and Shelton for highest weight modules. Connections with two different flag variety decompositions are discussed.

Author : Takehiko Yamanouchi
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 43,7 Mb
Release : 1993
Category : Duality theory
ISBN : 9780821825457

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Duality for Actions and Coactions of Measured Groupoids on von Neumann Algebras by Takehiko Yamanouchi Pdf

Through classification of compact abelian group actions on semifinite injective factors, Jones and Takesaki introduced a notion of an action of a measured groupoid on a von Neumann algebra, which was proven to be an important tool for such an analysis. In this paper, elaborating their definition, the author introduces a new concept of a measured groupoid action that may fit more perfectly in the groupoid setting. The author also considers a notion of a coaction of a measured groupoid by showing the existence of a canonical "coproduct" on every groupoid von Neumann algebra.

Author : Robert Gordon
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 54,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825433

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G-categories by Robert Gordon Pdf

A $G$-category is a category on which a group $G$ acts. This work studies the $2$-category $G$-Cat of $G$-categories, $G$-functors (functors which commute with the action of $G$ ) and $G$-natural transformations (natural transformations which commute with the $G$-action). There is particular emphasis on the relationship between a $G$-category and its stable subcategory, the largest sub-$G$-category on which $G$ operates trivially. Also contained here are some very general applications of the theory to various additive $G$-categories and to $G$-topoi.

Author : Vincent Cossart,Uwe Jannsen,Shuji Saito
Publisher : Springer Nature
Page : 258 pages
File Size : 52,9 Mb
Release : 2020-08-27
Category : Mathematics
ISBN : 9783030526405

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Desingularization: Invariants and Strategy by Vincent Cossart,Uwe Jannsen,Shuji Saito Pdf

This book provides a rigorous and self-contained review of desingularization theory. Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka’s Theory. The core of the book is a complete proof of desingularization of surfaces; despite being well-known, this result was no more than folklore for many years, with no existing references. Throughout the book there are numerous computations on standard bases, blowing ups and characteristic polyhedra, which will be a source of inspiration for experts exploring bigger dimensions. Beginners will also benefit from a section which presents some easily overlooked pathologies.

Author : Michael L. Mihalik,Steven Thomas Tschantz
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 41,7 Mb
Release : 1992
Category : Free products
ISBN : 9780821825310

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Semistability of Amalgamated Products and HNN-Extensions by Michael L. Mihalik,Steven Thomas Tschantz Pdf

In this work, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work.

Author : Thomas Callister Hales
Publisher : American Mathematical Soc.
Page : 142 pages
File Size : 44,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825396

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The Subregular Germ of Orbital Integrals by Thomas Callister Hales Pdf

Langlands theory predicts deep relationships between representations of different reductive groups over a local or global field. The trace formula attempts to reduce many such relationships to problems concerning conjugacy classes and integrals over conjugacy classes (orbital integrals) on $p$-adic groups. It is possible to reformulate these problems as ones in algebraic geometry by associating a variety $Y$ to each reductive group. Using methods of Igusa, the geometrical properties of the variety give detailed information about the asymptotic behavior of integrals over conjugacy classes.This monograph constructs the variety $Y$ and describes its geometry. As an application, the author uses the variety to give formulas for the leading terms (regular and subregular germs) in the asymptotic expansion of orbital integrals over $p$-adic fields. The final chapter shows how the properties of the variety may be used to confirm some predictions of Langlands theory on orbital integrals, Shalika germs, and endoscopy.

Author : Ian Anderson,Gerard Thompson
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 54,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825334

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The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations by Ian Anderson,Gerard Thompson Pdf

This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centers on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coincides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. What emerges is a fundamental dichotomy between second and higher order systems: the most general Lagrangian for any higher order system can depend only upon finitely many constants. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. A number of new examples illustrate the effectiveness of this approach. The monograph also contains a study of the inverse problem for a pair of geodesic equations arising from a two dimensional symmetric affine connection. The various possible solutions to the inverse problem for these equations are distinguished by geometric properties of the Ricci tensor.

Author : Francisco González-Acuña,Wilbur Carrington Whitten
Publisher : American Mathematical Soc.
Page : 55 pages
File Size : 54,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825341

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Imbeddings of Three-Manifold Groups by Francisco González-Acuña,Wilbur Carrington Whitten Pdf

This work deals with the two broad questions of how three-manifold groups imbed in one another and how such imbeddings relate to any corresponding $\pi _1$-injective maps. The focus is on when a given three-manifold covers another given manifold. In particular, the authors are concerned with 1) determining which three-manifold groups are not cohopfian--that is, which three-manifold groups imbed properly in themselves; 2) finding the knot subgroups of a knot group; and 3) investigating when surgery on a knot $K$ yields lens (or ``lens-like'') spaces and how this relates to the knot subgroup structure of $\pi _1(S^3-K)$. The authors use the formulation of a deformation theorem for $\pi _1$-injective maps between certain kinds of Haken manifolds and develop some algebraic tools.

Author : Dennis A. Hejhal
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 44,9 Mb
Release : 1992
Category : Automorphic functions
ISBN : 9780821825297

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Eigenvalues of the Laplacian for Hecke Triangle Groups by Dennis A. Hejhal Pdf

Paper I is concerned with computational aspects of the Selberg trace formalism, considering the usual type of eigenfunction and including an analysis of pseudo cusp forms and their residual effects. Paper II examines the modular group PSL (2, [bold]Z), as such groups have both a discrete and continuous spectrum. This paper only examines the discrete side of the spectrum.

Author : Kazuaki Taira
Publisher : American Mathematical Soc.
Page : 65 pages
File Size : 44,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821825358

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On the Existence of Feller Semigroups with Boundary Conditions by Kazuaki Taira Pdf

This monograph provides a careful and accessible exposition of functional analytic methods in stochastic analysis. The author focuses on the relationship among three subjects in analysis: Markov processes, Feller semigroups, and elliptic boundary value problems. The approach here is distinguished by the author's extensive use of the theory of partial differential equations. Filling a mathematical gap between textbooks on Markov processes and recent developments in analysis, this work describes a powerful method capable of extensive further development. The book would be suitable as a textbook in a one-year, advanced graduate course on functional analysis and partial differential equations, with emphasis on their strong interrelations with probability theory.