2 edition of **Commutative algebra and its connections to geometry** found in the catalog.

Commutative algebra and its connections to geometry

Pan-American Advanced Studies Institute (2009 Universidade Federal de Pernambuco)

- 32 Want to read
- 12 Currently reading

Published
**2011**
by American Mathematical Society in Providence, R.I
.

Written in English

- Commutative algebra -- Homological methods -- Syzygies, resolutions, complexes,
- Algebraic geometry -- Surfaces and higher-dimensional varieties -- Vector bundles on surfaces and higher-dimensional varieties, and their moduli,
- Homological Algebra,
- Algebraic Geometry,
- Commutative algebra -- Homological methods -- Homological functors on modules (Tor, Ext, etc.).,
- Algebraic geometry -- Special varieties -- Determinantal varieties,
- Algebraic geometry -- Cycles and subschemes -- Parametrization (Chow and Hilbert schemes),
- Commutative algebra -- Theory of modules and ideals -- Linkage, complete intersections and determinantal ideals,
- Algebraic geometry -- Projective and enumerative geometry -- Projective techniques,
- Congresses,
- Combinatorial group theory,
- Commutative algebra -- Homological methods -- Hilbert-Samuel and Hilbert-Kunz functions; PoincarÃ© series,
- Combinatorics -- Graph theory -- Applications

**Edition Notes**

Includes bibliographical references.

Statement | Olinda, Brazil, Alberto Corso, Claudia Polini, editors |

Series | Contemporary mathematics -- v. 555 |

Contributions | Corso, Alberto, Polini, Claudia, 1966- |

Classifications | |
---|---|

LC Classifications | QA182.5 .P36 2009 |

The Physical Object | |

Pagination | xvi, 215 p. : |

Number of Pages | 215 |

ID Numbers | |

Open Library | OL25162181M |

ISBN 10 | 9780821849590 |

LC Control Number | 2011027283 |

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry.4/5(27). Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and .

My research interests are focused on commutative algebra and its connections to neighbor fields such as algebraic K-theory or algebraic geometry. One of the motivations for my research is a group of questions informally known as "the homological conjectures". This book aims to introduce the reader to contemporary algebraic geometry and its necessary foundations in commutative algebra. It is self-contained, and touches on major themes that do not appear in many introductory books, such as schemes and the Riemann-Roch Theorem.

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics. Along the lines developed by Grothendieck, this book delves into the rich. A Term of Commutative Algebra. This book is a clear, concise, and efficient textbook, aimed at beginners, with a good selection of topics. Topics covered includes: Rings and Ideals, Radicals, Filtered Direct Limits, Cayley–Hamilton Theorem, Localization of Rings and Modules, Krull–Cohen–Seidenberg Theory, Rings and Ideals, Direct Limits, Filtered direct limit.

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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 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,at the Universidade Federal de Pernambuco in Olinda, Brazil.

The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections 4/5(1).

He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory.

The book contains numerous examples and exercises illustrating the by: A separate part deals with the necessary prerequisites from commutative algebra.

On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the : Springer-Verlag London.

Commutative algebra and algebraic geometry are extremely difficult subjects requiring a great deal of background. This book is written as a sort of intermediary text between introductory abstract algebra books with a full and exposition of algebraic structures, and advanced, highly technical texts that can be difficult to follow and grasp on a technical level.

This is not to say that no one else cares about my "great 21st century commutative algebra book". I have gotten a lot of feedback to the contrary, and I do think it -- or rather, parts of it -- are being read by a worldwide audience.

Conversely, I regularly peruse other people's great 21st century commutative algebra books for nuggets of insight. The book "Introduction to Commutative Algebra" (by Atiyah-Macdonald) is a good starting point; but if it seems difficult for you, you can consult with the book "Steps in Commutative Algebra" (by Sharp), which goes more in details.

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. 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. Commutative algebra and its connections to geometry: Pan-American Advanced Studies Institute, August, Universidade Federal de Pernambuco, Olinda, Brazil.

A Primer of Commutative Algebra James S. Milne Mav Abstract These notes collect the basic results in commutative algebra used in the rest of my notes and books. Although most of the material is standard, the notes include a few results, for example, the afﬁne version of Zariski’s main theorem, that are difﬁcult to ﬁnd.

This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch.

Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Commutative Algebra: with a View Toward Algebraic Geometry David Eisenbud (auth.) This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics.

"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 Commutative Algebra with a View Toward Algebraic Geometry "This text has personality―Those familiar with Eisenbud"s own research will recognize its traces in his choice of topics and manner of approach.

The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible/5(3).

Commutative Algebra with a View Toward Algebraic Geometry "This text has personality―Those familiar with Eisenbud"s own research will recognize its traces in his choice of topics and manner of approach.

The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible."―MATHEMATICAL REVIEWS4/5(25). Commutative Algebra with a View Toward Algebraic Geometry "This text has personality—Those familiar with Eisenbud"s own research will recognize its traces in his choice of topics and manner of approach.

The book conveys infectious enthusiasm and the conviction that research in the field is active and yet accessible."—MATHEMATICAL REVIEWSBrand: Springer New York. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry.

To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Overview. Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry.

In algebraic number theory, the rings of algebraic integers are Dedekind rings, which constitute therefore an important class of commutative erations related to modular arithmetic have led to the notion of a valuation ring.

Kunz says in the Foreword to the book that “[its] center of gravity lies more in commutative algebra than in algebraic geometry. For a continued study of algebraic geometry I recommend one of the excellent books that have recently appeared ”.A SINGULAR Introduction to Commutative Algebra oﬀers a rigorous intro-duction to commutative algebra and, at the same time, provides algorithms and computational practice.

In this book, we do not separate the theoretical and the computational part. Coincidentally, as new concepts are introduced,File Size: 6MB.BibTeX @MISC{Villarreal09commutativealgebra, author = {Rafael H. Villarreal and Departmento De Matemáticas and A.

Simis and W. V. Vasconcelos and J. Algebra}, title = {Commutative Algebra and its connections to Geometry Torsion freeness of edge ideals Maximal Cliques of Comparability Graphs Symbolic Rees algebras Sliding depth for trees The main reference: Reference}, year = {}}.