Equimultiplicity And Blowing Up

Author : Manfred Herrmann,Shin Ikeda,Ulrich Orbanz
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642613494

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Equimultiplicity and Blowing Up by Manfred Herrmann,Shin Ikeda,Ulrich Orbanz Pdf

Content and Subject Matter: This research monograph deals with two main subjects, namely the notion of equimultiplicity and the algebraic study of various graded rings in relation to blowing ups. Both subjects are clearly motivated by their use in resolving singularities of algebraic varieties, for which one of the main tools consists in blowing up the variety along an equimultiple subvariety. For equimultiplicity a unified and self-contained treatment of earlier results of two of the authors is given, establishing a notion of equimultiplicity for situations other than the classical ones. For blowing up, new results are presented on the connection with generalized Cohen-Macaulay rings. To keep this part self-contained too, a section on local cohomology and local duality for graded rings and modules is included with detailed proofs. Finally, in an appendix, the notion of equimultiplicity for complex analytic spaces is given a geometric interpretation and its equivalence to the algebraic notion is explained. The book is primarily addressed to specialists in the subject but the self-contained and unified presentation of numerous earlier results make it accessible to graduate students with basic knowledge in commutative algebra.

Author : B. Moonen,Manfred Herrmann,Shin Ikeda
Publisher : Unknown
Page : 656 pages
File Size : 48,8 Mb
Release : 1988-06-28
Category : Electronic
ISBN : 3642613500

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Equimultiplicity and Blowing Up by B. Moonen,Manfred Herrmann,Shin Ikeda Pdf

Author : Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps
Publisher : Springer
Page : 604 pages
File Size : 48,8 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9783319968278

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps Pdf

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.

Author : Robin Hartshorne,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 658 pages
File Size : 42,9 Mb
Release : 1975-12-31
Category : Mathematics
ISBN : 9780821814291

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Algebraic Geometry, Arcata 1974 by Robin Hartshorne,American Mathematical Society Pdf

Author : David Ellwood,Herwig Hauser,Shigefumi Mori,Josef Schicho
Publisher : American Mathematical Soc.
Page : 353 pages
File Size : 51,7 Mb
Release : 2014-12-12
Category : Mathematics
ISBN : 9780821889824

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The Resolution of Singular Algebraic Varieties by David Ellwood,Herwig Hauser,Shigefumi Mori,Josef Schicho Pdf

Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Author : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 41,9 Mb
Release : 2005-05-23
Category : Mathematics
ISBN : 3540255400

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Integral Closure by Wolmer Vasconcelos Pdf

This book gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. It gives a comprehensive treatment of Rees algebras and multiplicity theory while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.

Author : Winfried Bruns,H. Jürgen Herzog
Publisher : Cambridge University Press
Page : 471 pages
File Size : 40,7 Mb
Release : 1998-06-18
Category : Mathematics
ISBN : 9780521566742

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Cohen-Macaulay Rings by Winfried Bruns,H. Jürgen Herzog Pdf

In the last two decades Cohen-Macaulay rings and modules have been central topics in commutative algebra. This book meets the need for a thorough, self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules. A separate chapter is devoted to Hilbert functions (including Macaulay's theorem) and numerical invariants derived from them. The authors emphasize the study of explicit, specific rings, making the presentation as concrete as possible. So the general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. Their connections with combinatorics are highlighted, e.g. Stanley's upper bound theorem or Ehrhart's reciprocity law for rational polytopes. The final chapters are devoted to Hochster's theorem on big Cohen-Macaulay modules and its applications, including Peskine-Szpiro's intersection theorem, the Evans-Griffith syzygy theorem, bounds for Bass numbers, and tight closure. Throughout each chapter the authors have supplied many examples and exercises which, combined with the expository style, will make the book very useful for graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.

Author : Aron Simis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 370 pages
File Size : 48,6 Mb
Release : 2023-08-07
Category : Mathematics
ISBN : 9783111078786

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Commutative Algebra by Aron Simis Pdf

The primary audience for this book is students and the young researchers interested in the core of the discipline. Commutative algebra is by and large a self-contained discipline, which makes it quite dry for the beginner with a basic training in elementary algebra and calculus. A stable mathematical discipline such as this enshrines a vital number of topics to be learned at an early stage, more or less universally accepted and practiced. Naturally, authors tend to turn these topics into an increasingly short and elegant list of basic facts of the theory. So, the shorter the better. However, there is a subtle watershed between elegance and usefulness, especially if the target is the beginner. From my experience throughout years of teaching, elegance and terseness do not do it, except much later in the carrier. To become useful, the material ought to carry quite a bit of motivation through justification and usefulness pointers. On the other hand, it is difficult to contemplate these teaching devices in the writing of a short book. I have divided the material in three parts. starting with more elementary sections, then carrying an intermezzo on more difficult themes to make up for a smooth crescendo with additional tools and, finally, the more advanced part, versing on a reasonable chunk of present-day steering of commutative algebra. Historic notes at the end of each chapter provide insight into the original sources and background information on a particular subject or theorem. Exercises are provided and propose problems that apply the theory to solve concrete questions (yes, with concrete polynomials, and so forth).

Author : Herwig Hauser,Joseph Lipman,Frans Oort,Adolfo Quiros
Publisher : Birkhäuser
Page : 610 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883993

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Resolution of Singularities by Herwig Hauser,Joseph Lipman,Frans Oort,Adolfo Quiros Pdf

In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

Author : William J. Heinzer,Judith D. Sally
Publisher : American Mathematical Soc.
Page : 456 pages
File Size : 42,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851883

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Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra by William J. Heinzer,Judith D. Sally Pdf

This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra.

Author : Vladimir I. Arnold,Gert-Martin Greuel,Joseph H.M. Steenbrink
Publisher : Birkhäuser
Page : 475 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887700

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Singularities by Vladimir I. Arnold,Gert-Martin Greuel,Joseph H.M. Steenbrink Pdf

In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.

Author : Giuseppe Valla,Ngo Viet Trung,Aron Simis
Publisher : World Scientific
Page : 330 pages
File Size : 49,7 Mb
Release : 1994-08-19
Category : Electronic
ISBN : 9789814551793

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Commutative Algebra - Proceedings Of The Workshop by Giuseppe Valla,Ngo Viet Trung,Aron Simis Pdf

In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools.One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results.At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra — such as deformation, linkage, algebraic tori and determinantal rings, etc.This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.

Author : Shirō Gotō,Koji Nishida
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 43,8 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.

Author : Richard N. Draper
Publisher : CRC Press
Page : 308 pages
File Size : 44,8 Mb
Release : 1982-04-28
Category : Mathematics
ISBN : 082471282X

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Analytic Methods in Commutative Algebra by Richard N. Draper Pdf

Author : Wolmer V. Vasconcelos
Publisher : Cambridge University Press
Page : 343 pages
File Size : 43,8 Mb
Release : 1994-02-25
Category : Mathematics
ISBN : 9780521454841

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Arithmetic of Blowup Algebras by Wolmer V. Vasconcelos Pdf

This book discusses recent developments in an important area of computational commutative algebra.