Three Lectures On Commutative Algebra

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Three Lectures On Commutative Algebra

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Author : Holger Brenner
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Three Lectures On Commutative Algebra written by Holger Brenner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

These lectures provides detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications: tight closure and vector bundles; combinatorics and commutative algebra; constructive desingularization."

Three Lectures On Commutative Algebra

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Author : Holger Brenner
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Three Lectures On Commutative Algebra written by Holger Brenner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This book provides careful and detailed introductions to some of the latest advances in three significant areas of rapid development in commutative algebra and its applications. The book is based on courses at the Winter School on Commutative Algebra and Applications held in Barcelona: Tight closure and vector bundles, by H. Brenner; Combinatorics and commutative algebra, by J. Herzog; and Constructive desingularization, by O. Villamayor.

Lectures On Algebraic Geometry Ii

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Author : Günter Harder
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-21

Lectures On Algebraic Geometry Ii written by Günter Harder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-21 with Mathematics categories.

This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

Lectures On Rings And Modules

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Author : Joachim Lambek
language : en
Publisher:
Release Date : 1966

Lectures On Rings And Modules written by Joachim Lambek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Associative rings categories.

Koszul Cohomology And Algebraic Geometry

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Author : Marian Aprodu
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Koszul Cohomology And Algebraic Geometry written by Marian Aprodu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

The systematic use of Koszul cohomology computations in algebraic geometry can be traced back to the foundational work of Mark Green in the 1980s. Green connected classical results concerning the ideal of a projective variety with vanishing theorems for Koszul cohomology. Green and Lazarsfeld also stated two conjectures that relate the Koszul cohomology of algebraic curves with the existence of special divisors on the curve. These conjectures became an important guideline for future research. In the intervening years, there has been a growing interaction between Koszul cohomology and algebraic geometry. Green and Voisin applied Koszul cohomology to a number of Hodge-theoretic problems, with remarkable success. More recently, Voisin achieved a breakthrough by proving Green's conjecture for general curves; soon afterwards, the Green-Lazarsfeld conjecture for general curves was proved as well. This book is primarily concerned with applications of Koszul cohomology to algebraic geometry, with an emphasis on syzygies of complex projective curves. The authors' main goal is to present Voisin's proof of the generic Green conjecture, and subsequent refinements. They discuss the geometric aspects of the theory and a number of concrete applications of Koszul cohomology to problems in algebraic geometry, including applications to Hodge theory and to the geometry of the moduli space of curves.

Residues And Duality For Projective Algebraic Varieties

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Author : Ernst Kunz
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Residues And Duality For Projective Algebraic Varieties written by Ernst Kunz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D. A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."--BOOK JACKET.

Robert Steinberg

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Author : Robert Steinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-22

Robert Steinberg written by Robert Steinberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Mathematics categories.

Robert Steinberg's Lectures on Chevalley Groups were delivered and written during the author's sabbatical visit to Yale University in the 1967–1968 academic year. The work presents the status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in the subsequent classification of finite groups. This posthumous edition incorporates additions and corrections prepared by the author during his retirement, including a new introductory chapter. A bibliography and editorial notes have also been added.

Combinatorial Commutative Algebra

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Author : Ezra Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-21

Combinatorial Commutative Algebra written by Ezra Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.

Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Quantum Field Theory Batalin Vilkovisky Formalism And Its Applications

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Author : Pavel Mnev
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-20

Quantum Field Theory Batalin Vilkovisky Formalism And Its Applications written by Pavel Mnev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-20 with Mathematics categories.

This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.

Polynomial Methods In Combinatorics

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Author : Larry Guth
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-10

Polynomial Methods In Combinatorics written by Larry Guth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-10 with Mathematics categories.

This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdős's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.