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On Cohen Macaulay Local Rings Of Dimension One And Embedding Dimension Two
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Book Synopsis The Lefschetz Centennial Conference by : D. Sundararaman
Download or read book The Lefschetz Centennial Conference written by D. Sundararaman and published by American Mathematical Soc.. This book was released on 1986 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: A three-volume series of proceedings of the Solomon Lefschetz Centennial Conference, held in 1984 in Mexico City to celebrate Lefschetz's 100th birthday. The conference focused on three main areas of Lefschetz's research: algebraic geometry, algebraic topology, and differential geometry.
Book Synopsis Cohen-Macaulay Rings by : Winfried Bruns
Download or read book Cohen-Macaulay Rings written by Winfried Bruns and published by Cambridge University Press. This book was released on 1998-06-18 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proceedings of the 1984 Vancouver Conference in Algebraic Geometry by : James B. Carrell
Download or read book Proceedings of the 1984 Vancouver Conference in Algebraic Geometry written by James B. Carrell and published by American Mathematical Soc.. This book was released on 1986 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers a cross-section of the developments in modern algebraic geometry. This work covers topics including algebraic groups and representation theory, enumerative geometry, Schubert varieties, rationality, compactifications and surfaces.
Book Synopsis On the Homology of Local Cohen-Macaulay Rings by : Alan B. Evans
Download or read book On the Homology of Local Cohen-Macaulay Rings written by Alan B. Evans and published by . This book was released on 1979 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Special Conditions on Maximal Cohen-Macaulay Modules, and Applications to the Theory of Multiplicities by : Douglas Hanes
Download or read book Special Conditions on Maximal Cohen-Macaulay Modules, and Applications to the Theory of Multiplicities written by Douglas Hanes and published by . This book was released on 1999 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Commutative Algebra and Its Connections to Geometry by : Alberto Corso
Download or read book Commutative Algebra and Its Connections to Geometry written by Alberto Corso and published by American Mathematical Soc.. This book was released on 2011-10-20 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Cohen-Macaulay Representations by : Graham J. Leuschke
Download or read book Cohen-Macaulay Representations written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2012-05-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.
Book Synopsis Hilbert Functions of Filtered Modules by : Maria Evelina Rossi
Download or read book Hilbert Functions of Filtered Modules written by Maria Evelina Rossi and published by Springer Science & Business Media. This book was released on 2010-08-25 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They capture many useful numerical characters associated to a projective variety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one place many new developments of this theory by using a unifying approach which gives self-contained and easier proofs. The extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two of the main features of the monograph. The material is intended for graduate students and researchers who are interested in Commutative Algebra, in particular in the theory of the Hilbert Functions and related topics.
Book Synopsis Syzygies and Hilbert Functions by : Irena Peeva
Download or read book Syzygies and Hilbert Functions written by Irena Peeva and published by CRC Press. This book was released on 2007-03-20 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Integral Closure by : Wolmer Vasconcelos
Download or read book Integral Closure written by Wolmer Vasconcelos and published by Springer Science & Business Media. This book was released on 2005-11-04 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Commutative Ring Theory by : Hideyuki Matsumura
Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MA THEMA TICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis The Use of Ultraproducts in Commutative Algebra by : Hans Schoutens
Download or read book The Use of Ultraproducts in Commutative Algebra written by Hans Schoutens and published by Springer. This book was released on 2010-07-16 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zero characteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Resolution of Curve and Surface Singularities in Characteristic Zero by : K. Kiyek
Download or read book Resolution of Curve and Surface Singularities in Characteristic Zero written by K. Kiyek and published by Springer Science & Business Media. This book was released on 2012-09-11 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
Book Synopsis Lectures on Resolution of Singularities (AM-166) by : János Kollár
Download or read book Lectures on Resolution of Singularities (AM-166) written by János Kollár and published by Princeton University Press. This book was released on 2009-01-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.
Book Synopsis Six Lectures on Commutative Algebra by : J. Elias
Download or read book Six Lectures on Commutative Algebra written by J. Elias and published by Springer Science & Business Media. This book was released on 2010-03-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
