Minimal Free Resolutions Over Complete Intersections

Author : David Eisenbud,Irena Peeva
Publisher : Springer
Page : 107 pages
File Size : 50,6 Mb
Release : 2016-03-08
Category : Mathematics
ISBN : 9783319264370

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Minimal Free Resolutions over Complete Intersections by David Eisenbud,Irena Peeva Pdf

This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a non-zero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

Author : Joe Harris
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 42,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475721898

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Algebraic Geometry by Joe Harris Pdf

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

Author : David Eisenbud,Srikanth B. Iyengar,Anurag K. Singh,J. Toby Stafford,Michel Van den Bergh
Publisher : Cambridge University Press
Page : 463 pages
File Size : 46,5 Mb
Release : 2015-11-19
Category : Mathematics
ISBN : 9781107065628

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Commutative Algebra and Noncommutative Algebraic Geometry by David Eisenbud,Srikanth B. Iyengar,Anurag K. Singh,J. Toby Stafford,Michel Van den Bergh Pdf

This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 1 contains expository papers ideal for those entering the field.

Author : J. Elias,J. M. Giral,Rosa M. Miró-Roig,Santiago Zarzuela
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 45,9 Mb
Release : 2010-03-17
Category : Mathematics
ISBN : 9783034603294

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Six Lectures on Commutative Algebra by J. Elias,J. M. Giral,Rosa M. Miró-Roig,Santiago Zarzuela Pdf

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH

Author : David Eisenbud,Craig Huneke
Publisher : CRC Press
Page : 160 pages
File Size : 43,6 Mb
Release : 2023-05-31
Category : Mathematics
ISBN : 9781000945249

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Free Resolutions in Commutative Algebra and Algebraic Geometry by David Eisenbud,Craig Huneke Pdf

The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future developments in the field.

Author : Laura Costa,Rosa María Miró-Roig,Joan Pons-Llopis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 282 pages
File Size : 41,7 Mb
Release : 2021-05-10
Category : Mathematics
ISBN : 9783110647686

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Ulrich Bundles by Laura Costa,Rosa María Miró-Roig,Joan Pons-Llopis Pdf

The goal of this book is to cover the active developments of arithmetically Cohen-Macaulay and Ulrich bundles and related topics in the last 30 years, and to present relevant techniques and multiple applications of the theory of Ulrich bundles to a wide range of problems in algebraic geometry as well as in commutative algebra.

Author : Jan Oddvar Kleppe,Juan C. Migliore,Rosa Miró-Roig
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 43,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827383

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Gorenstein Liaison, Complete Intersection Liaison Invariants and Unobstructedness by Jan Oddvar Kleppe,Juan C. Migliore,Rosa Miró-Roig Pdf

This paper contributes to the liaison and obstruction theory of subschemes in $\mathbb{P}^n$ having codimension at least three. The first part establishes several basic results on Gorenstein liaison. A classical result of Gaeta on liaison classes of projectively normal curves in $\mathbb{P}^3$ is generalized to the statement that every codimension $c$ ""standard determinantal scheme"" (i.e. a scheme defined by the maximal minors of a $t\times (t+c-1)$ homogeneous matrix), is in the Gorenstein liaison class of a complete intersection. Then Gorenstein liaison (G-liaison) theory is developed as a theory of generalized divisors on arithmetically Cohen-Macaulay schemes. In particular, a rather general construction of basic double G-linkage is introduced, which preserves the even G-liaison class.This construction extends the notion of basic double linkage, which plays a fundamental role in the codimension two situation. The second part of the paper studies groups which are invariant under complete intersection linkage, and gives a number of geometric applications of these invariants. Several differences between Gorenstein and complete intersection liaison are highlighted. For example, it turns out that linearly equivalent divisors on a smooth arithmetically Cohen-Macaulay subscheme belong, in general, to different complete intersection liaison classes, but they are always contained in the same even Gorenstein liaison class. The third part develops the interplay between liaison theory and obstruction theory and includes dimension estimates of various Hilbert schemes. For example, it is shown that most standard determinantal subschemes of codimension $3$ are unobstructed, and the dimensions of their components in the corresponding Hilbert schemes are computed.

Author : Nicholas R. Baeth,Thiago H. Freitas,Graham J. Leuschke,Victor H. Jorge Pérez
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 47,5 Mb
Release : 2021-10-06
Category : Education
ISBN : 9781470456016

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Commutative Algebra: 150 Years with Roger and Sylvia Wiegand by Nicholas R. Baeth,Thiago H. Freitas,Graham J. Leuschke,Victor H. Jorge Pérez Pdf

This volume contains the combined Proceedings of the Second International Meeting on Commutative Algebra and Related Areas (SIMCARA) held from July 22–26, 2019, at the Universidade de São Paulo, São Carlos, Brazil, and the AMS Special Session on Commutative Algebra, held from September 14–15, 2019, at the University of Wisconsin-Madison, Wisconsin. These two meetings celebrated the combined 150th birthday of Roger and Sylvia Wiegand. The Wiegands have been a fixture in the commutative algebra community, as well as the wider mathematical community, for over 40 years. Articles in this volume cover various areas of factorization theory, homological algebra, ideal theory, representation theory, homological rigidity, maximal Cohen-Macaulay modules, and the behavior of prime spectra under completion, as well as some topics in related fields. The volume itself bears evidence that the area of commutative algebra is a vibrant one and highlights the influence of the Wiegands on generations of researchers. It will be useful to researchers and graduate students.

Author : Izzet Coskun,Tommaso de Fernex,Angela Gibney
Publisher : American Mathematical Soc.
Page : 370 pages
File Size : 43,8 Mb
Release : 2017-07-12
Category : $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions
ISBN : 9781470435578

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Surveys on Recent Developments in Algebraic Geometry by Izzet Coskun,Tommaso de Fernex,Angela Gibney Pdf

The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

Author : Claudia Miller,Janet Striuli,Emily E. Witt
Publisher : Springer Nature
Page : 439 pages
File Size : 46,7 Mb
Release : 2022-03-18
Category : Mathematics
ISBN : 9783030919863

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Women in Commutative Algebra by Claudia Miller,Janet Striuli,Emily E. Witt Pdf

This volume features contributions from the Women in Commutative Algebra (WICA) workshop held at the Banff International Research Station (BIRS) from October 20-25, 2019, run by the Pacific Institute of Mathematical Sciences (PIMS). The purpose of this meeting was for groups of mathematicians to work on joint research projects in the mathematical field of Commutative Algebra and continue these projects together long-distance after its close. The chapters include both direct results and surveys, with contributions from research groups and individual authors. The WICA conference was the first of its kind in the large and vibrant area of Commutative Algebra, and this volume is intended to showcase its important results and to encourage further collaboration among marginalized practitioners in the field. It will be of interest to a wide range of researchers, from PhD students to senior experts.

Author : Irena Peeva
Publisher : CRC Press
Page : 305 pages
File Size : 55,7 Mb
Release : 2007-03-20
Category : Mathematics
ISBN : 9781420050912

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Syzygies and Hilbert Functions by Irena Peeva Pdf

Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts.

Author : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 46,5 Mb
Release : 2001-09-25
Category : Mathematics
ISBN : 3540422307

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Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels Pdf

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Author : Anonim
Publisher : Unknown
Page : 776 pages
File Size : 44,5 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015069723800

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 390 pages
File Size : 54,8 Mb
Release : 2008
Category : Algebra
ISBN : UOM:39015072631461

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Algebra Colloquium by Anonim Pdf

Author : Irena Peeva
Publisher : Springer Nature
Page : 898 pages
File Size : 44,9 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030896942

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Commutative Algebra by Irena Peeva Pdf

This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra. The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.