Commutative Algebra And Its Connections To Geometry

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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.

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Genre : Mathematics
Author : Alberto Corso
Publisher : American Mathematical Soc.
Release : 2011-10-20
File : 233 Pages
ISBN-13 : 9780821849590


Commutative Algebra And Algebraic Geometry

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The first Joint AMS-India Mathematics Meeting was held in Bangalore (India). This book presents articles written by speakers from a special session on commutative algebra and algebraic geometry. Included are contributions from some leading researchers around the world in this subject area. The volume contains new and original research papers and survey articles suitable for graduate students and researchers interested in commutative algebra and algebraic geometry.

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Genre : Mathematics
Author : Sudhir Ghorpade
Publisher : American Mathematical Soc.
Release : 2005
File : 192 Pages
ISBN-13 : 9780821836293


Algebraic Geometry And Commutative Algebra

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Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from power series rings and rings of invariants of finite linear groups to the convolution algebra of distributions on totally disconnected locally compact groups. The discussion begins with a description of several formulas for enumerating certain types of objects, which may be tabular arrangements of integers called Young tableaux or some types of monomials. The next chapter explains how to establish these enumerative formulas, with emphasis on the role played by transformations of determinantal polynomials and recurrence relations satisfied by them. The book then turns to several applications of the enumerative formulas and universal identity, including including enumerative proofs of the straightening law of Doubilet-Rota-Stein and computations of Hilbert functions of polynomial ideals of certain determinantal loci. Invariant differentials and quaternion extensions are also examined, along with the moduli of Todorov surfaces and the classification problem of embedded lines in characteristic p. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.

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Genre : Mathematics
Author : Hiroaki Hijikata
Publisher : Academic Press
Release : 2014-05-10
File : 417 Pages
ISBN-13 : 9781483265186


Connections Between Algebra Combinatorics And Geometry

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Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resource for graduate students and researchers who wish to expand their knowledge of commutative algebra, algebraic geometry, combinatorics, and the intricacies of their intersection.

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Genre : Mathematics
Author : Susan M. Cooper
Publisher : Springer
Release : 2014-05-16
File : 328 Pages
ISBN-13 : 9781493906260


Encyclopaedia Of Mathematics Set

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The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.

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Genre : Mathematics
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Release : 1994-02-28
File : 982 Pages
ISBN-13 : 1556080107


Commutative Algebra And Noncommutative Algebraic Geometry

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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.

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Genre : Mathematics
Author : David Eisenbud
Publisher : Cambridge University Press
Release : 2015-11-19
File : 463 Pages
ISBN-13 : 9781107065628


Introduction To Algebraic Geometry And Commutative Algebra

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Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.

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Genre : Mathematics
Author : Dilip P. Patil
Publisher : World Scientific
Release : 2010
File : 220 Pages
ISBN-13 : 9789814304573


Advanced Algebra

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Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.

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Genre : Mathematics
Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Release : 2007-10-11
File : 754 Pages
ISBN-13 : 9780817646134


Commutative Algebra And Algebraic Geometry

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Contains contributions by over 25 leading international mathematicians in the areas of commutative algebra and algebraic geometry. The text presents developments and results based on, and inspired by, the work of Mario Fiorentini. It covers topics ranging from almost numerical invariants of algebraic curves to deformation of projective schemes.

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Genre : Mathematics
Author : Freddy Van Oystaeyen
Publisher : CRC Press
Release : 1999-03-31
File : 340 Pages
ISBN-13 : 0824719905


Elementary Modular Iwasawa Theory

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This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows:Many open problems are presented to stimulate young researchers pursuing their field of study.

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Genre : Mathematics
Author : Haruzo Hida
Publisher : World Scientific
Release : 2021-10-04
File : 446 Pages
ISBN-13 : 9789811241383