Associated Graded Algebra Of A Gorenstein Artin Algebra

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Associated Graded Algebra of a Gorenstein Artin Algebra

Anthony A. Iarrobino
Associated Graded Algebra of a Gorenstein Artin Algebra Book PDF

Author : Anthony A. Iarrobino
Publisher : American Mathematical Soc.
Page : 115 pages
File Size : 43,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825761

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Associated Graded Algebra of a Gorenstein Artin Algebra by Anthony A. Iarrobino Pdf

In 1904, Macaulay described the Hilbert function of the intersection of two plane curve branches: It is the sum of a sequence of functions of simple form. This monograph describes the structure of the tangent cone of the intersection underlying this symmetry. Iarrobino generalizes Macaulay's result beyond complete intersections in two variables to Gorenstein Artin algebras in an arbitrary number of variables. He shows that the tangent cone of a Gorenstein singularity contains a sequence of ideals whose successive quotients are reflexive modules. Applications are given to determining the multiplicity and orders of generators of Gorenstein ideals and to problems of deforming singular mapping germs. Also included are a survey of results concerning the Hilbert function of Gorenstein Artin algebras and an extensive bibliography.

Associated Graded Algebra of a Gorenstein Artin Algebra

Anthony Ayers Iarrobino
Associated Graded Algebra of a Gorenstein Artin Algebra Book PDF

Author : Anthony Ayers Iarrobino
Publisher : Oxford University Press, USA
Page : 128 pages
File Size : 44,5 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 147040091X

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Associated Graded Algebra of a Gorenstein Artin Algebra by Anthony Ayers Iarrobino Pdf

In 1904, Macaulay described the Hilbert function of the intersection of two plane curve branches: It is the sum of a sequence of functions of simple form. This monograph describes the structure of the tangent cone of the intersections underlying this symmetry. Iarrobino generalizes Macaulay's result beyond complete intersections in two variables to Gorenstein Artin algebras in an arbitary number of variables. He shows that the tangent cone of a Gorenstein singularity contains a sequence of ideals whose successive quotients are reflexive modules. Applications are given to determining the multiplicity and orders of generators of Gorenstein ideals and to problems of deforming singular mapping germs. Also included are a survey of results concerning the Hilbert function of Gorenstein Artin algebras and an extensive bibliography.

Power Sums, Gorenstein Algebras, and Determinantal Loci

Anthony Iarrobino,Vassil Kanev
Power Sums Gorenstein Algebras and Determinantal Loci Book PDF

Author : Anthony Iarrobino,Vassil Kanev
Publisher : Springer
Page : 365 pages
File Size : 50,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540467076

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Power Sums, Gorenstein Algebras, and Determinantal Loci by Anthony Iarrobino,Vassil Kanev Pdf

This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.

Commutative Algebra

Melvin Hochster,Craig Huneke,Judith D. Sally
Commutative Algebra Book PDF

Author : Melvin Hochster,Craig Huneke,Judith D. Sally
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236603

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Commutative Algebra by Melvin Hochster,Craig Huneke,Judith D. Sally Pdf

During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley. The intent of the microprogram was to survey recent major results and current trends in the theory of commutative rings, especially commutative Noetherian rings. There was enthusiastic international participation. The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from the speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. The editors would like to express their appreciation to the director of MSRI, Professor Irving Kaplansky, who first suggested the possibility of such a conference and made the task of organization painless. We would also like to thank the IVISRI staff who were unfailingly efficient, pleasant, and helpful during the meeting, and the manager of MSRI, Arlene Baxter, for her help with this volume. Finally we would like to express our appreciation to David Mostardi who did much of the typing and put the electronic pieces together.

The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations

Shirō Gotō,Koji Nishida
The Cohen Macaulay and Gorenstein Rees Algebras Associated to Filtrations Book PDF

Author : Shirō Gotō,Koji Nishida
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 48,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825846

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The Cohen-Macaulay and Gorenstein Rees Algebras Associated to Filtrations by Shirō Gotō,Koji Nishida Pdf

This monograph consists of two parts. Part I investigates the Cohen-Macaulay and Gorenstein properties of symbolic Rees algebras for one-dimensional prime ideals in Cohen-Macaulay local rings. Practical criteria for these algebras to be Cohen-Macaulay and Gorenstein rings are described in terms of certain elements in the prime ideals. This framework is generalized in Part II to Rees algebras $R(F)$ and graded rings $G(F)$ associated to general filtrations of ideals in arbitrary Noetherian local rings. Goto and Nishida give certain cohomological characterizations for algebras $R(F)$ to be Cohen-Macaulay or Gorenstein rings in connection with the corresponding ring-theoretic properties of $G(F)$. In this way, readers follow a history of the development of the ring theory of Rees algebras. The book raises many important open questions.

Commutative Algebra and Its Connections to Geometry

Alberto Corso,Claudia Polini
Commutative Algebra and Its Connections to Geometry Book PDF

Author : Alberto Corso,Claudia Polini
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 46,7 Mb
Release : 2011-10-20
Category : Mathematics
ISBN : 9780821849590

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Commutative Algebra and Its Connections to Geometry by Alberto Corso,Claudia Polini Pdf

This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil. The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.

Commutative Algebra and its Interactions to Algebraic Geometry

Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG
Commutative Algebra and its Interactions to Algebraic Geometry Book PDF

Author : Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG
Publisher : Springer
Page : 258 pages
File Size : 43,6 Mb
Release : 2018-08-02
Category : Mathematics
ISBN : 9783319755656

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Commutative Algebra and its Interactions to Algebraic Geometry by Nguyen Tu CUONG,Le Tuan HOA,Ngo Viet TRUNG Pdf

This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.

Extended Abstracts Spring 2015

Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela
Extended Abstracts Spring 2015 Book PDF

Author : Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela
Publisher : Birkhäuser
Page : 192 pages
File Size : 45,5 Mb
Release : 2016-11-30
Category : Mathematics
ISBN : 9783319454412

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Extended Abstracts Spring 2015 by Dolors Herbera,Wolfgang Pitsch,Santiago Zarzuela Pdf

This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.

Algebra, $K$-Theory, Groups, and Education

Hyman Bass,Tsit-Yuen Lam,Andy Roy Magid
Algebra K Theory Groups and Education Book PDF

Author : Hyman Bass,Tsit-Yuen Lam,Andy Roy Magid
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 40,8 Mb
Release : 1999
Category : Algebra
ISBN : 9780821810873

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Algebra, $K$-Theory, Groups, and Education by Hyman Bass,Tsit-Yuen Lam,Andy Roy Magid Pdf

This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass, and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.

Introduction to Liaison Theory and Deficiency Modules

Juan C. Migliore
Introduction to Liaison Theory and Deficiency Modules Book PDF

Author : Juan C. Migliore
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217947

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Introduction to Liaison Theory and Deficiency Modules by Juan C. Migliore Pdf

In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks. I was asked to write a monograph based on my talks, and the result was published by the Global Analysis Research Center of that University in 1994. The monograph treated deficiency modules and liaison theory for complete intersections. Over the next several years I continually thought of improvements and additions that I would like to make to the manuscript, and at the same time my research led me in directions that gave me a fresh perspective on much of the material, especially in the direction of liaison theory. This re sulted in a dramatic change in the focus of this manuscript, from complete intersections to Gorenstein ideals, and a substantial amount of additions and revisions. It is my hope that this book now serves not only as an introduction to a beautiful subject, but also gives the reader a glimpse at very recent developments and an idea of the direction in which liaison theory is going, at least from my perspective. One theme which I have tried to stress is the tremendous amount of geometry which lies at the heart of the subject, and the beautiful interplay between algebra and geometry. Whenever possible I have given remarks and examples to illustrate this interplay, and I have tried to phrase the results in as geometric a way as possible.

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Lie Algebras Lie Superalgebras Vertex Algebras and Related Topics Book PDF

Author : Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 41,5 Mb
Release : 2016-06-28
Category : Group theory and generalizations
ISBN : 9781470418441

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Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics by Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall Pdf

This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Triangular Algebras and Ideals of Nest Algebras

John Lindsay Orr
Triangular Algebras and Ideals of Nest Algebras Book PDF

Author : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 49 pages
File Size : 54,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804056

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Triangular Algebras and Ideals of Nest Algebras by John Lindsay Orr Pdf

Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.

Hilbert Modules over Operator Algebras

Paul S. Muhly,Baruch Solel
Hilbert Modules over Operator Algebras Book PDF

Author : Paul S. Muhly,Baruch Solel
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 41,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803462

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Hilbert Modules over Operator Algebras by Paul S. Muhly,Baruch Solel Pdf

This book gives a general systematic analysis of the notions of ``projectivity'' and ``injectivity'' in the context of Hilbert modules over operator algebras. A Hilbert module over an operator algebra $A$ is simply the Hilbert space of a (contractive) representation of $A$ viewed as a module over $A$ in the usual way. In this work, Muhly and Solel introduce various notions of projective Hilbert modules and use them to investigate dilation and commutant lifting problems over certain infinite dimensional analogues of incidence algebras. The authors prove that commutant lifting holds for such an algebra if and only if the pattern indexing the algebra is a ``tree'' in the sense of computer directories.

Filtrations on the Homology of Algebraic Varieties

Eric M. Friedlander,Barry Mazur
Filtrations on the Homology of Algebraic Varieties Book PDF

Author : Eric M. Friedlander,Barry Mazur
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 42,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825914

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Filtrations on the Homology of Algebraic Varieties by Eric M. Friedlander,Barry Mazur Pdf

This work provides a detailed exposition of a classical topic from a very recent viewpoint. Friedlander and Mazur describe some foundational aspects of ``Lawson homology'' for complex projective algebraic varieties, a homology theory defined in terms of homotopy groups of spaces of algebraic cycles. Attention is paid to methods of group completing abelian topological monoids. The authors study properties of Chow varieties, especially in connection with algebraic correspondences relating algebraic varieties. Operations on Lawson homology are introduced and analyzed. These operations lead to a filtration on the singular homology of algebraic varieties, which is identified in terms of correspondences and related to classical filtrations of Hodge and Grothendieck.

Classification of Direct Limits of Even Cuntz-Circle Algebras

Huaxin Lin,Norman Christopher Phillips
Classification of Direct Limits of Even Cuntz Circle Algebras Book PDF

Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 49,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804032

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Classification of Direct Limits of Even Cuntz-Circle Algebras by Huaxin Lin,Norman Christopher Phillips Pdf

does not need NBB copy.