Cohomology Of Vector Bundles And Syzygies

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Cohomology of Vector Bundles and Syzygies

Author : Jerzy Weyman
Publisher : Cambridge University Press
ISBN 13 : 9780521621977
Total Pages : 404 pages
Book Rating : 4.6/5 (219 download)

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Book Synopsis Cohomology of Vector Bundles and Syzygies by : Jerzy Weyman

Download or read book Cohomology of Vector Bundles and Syzygies written by Jerzy Weyman and published by Cambridge University Press. This book was released on 2003-06-09 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

Vector Bundles and Representation Theory

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
ISBN 13 : 0821832646
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Vector Bundles and Representation Theory by : Steven Dale Cutkosky

Download or read book Vector Bundles and Representation Theory written by Steven Dale Cutkosky and published by American Mathematical Soc.. This book was released on 2003 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 13 papers from the conference on ``Hilbert Schemes, Vector Bundles and Their Interplay with Representation Theory''. The papers are written by leading mathematicians in algebraic geometry and representation theory and present the latest developments in the field. Among other contributions, the volume includes several very impressive and elegant theorems in representation theory by R. Friedman and J. W. Morgan, convolution on homology groups of moduli spaces of sheaves on K3 surfaces by H. Nakajima, and computation of the $S1$ fixed points in Quot-schemes and mirror principle computations for Grassmanians by S.-T. Yau, et al. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, topology and their applications to high energy physics.

Connections, Curvature, and Cohomology V1

Author :
Publisher : Academic Press
ISBN 13 : 9780080873602
Total Pages : 442 pages
Book Rating : 4.8/5 (736 download)

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Book Synopsis Connections, Curvature, and Cohomology V1 by :

Download or read book Connections, Curvature, and Cohomology V1 written by and published by Academic Press. This book was released on 1972-07-31 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Connections, Curvature, and Cohomology V1

Vector Bundles in Algebraic Geometry

Author : N. J. Hitchin
Publisher : Cambridge University Press
ISBN 13 : 0521498783
Total Pages : 359 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Vector Bundles in Algebraic Geometry by : N. J. Hitchin

Download or read book Vector Bundles in Algebraic Geometry written by N. J. Hitchin and published by Cambridge University Press. This book was released on 1995-03-16 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.

Vector Bundles and Their Applications

Author : Glenys Luke
Publisher : Springer Science & Business Media
ISBN 13 : 1475769237
Total Pages : 259 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Vector Bundles and Their Applications by : Glenys Luke

Download or read book Vector Bundles and Their Applications written by Glenys Luke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the basic notions of vector bundles and their applications. The focus of attention is towards explaining the most important notions and geometric constructions connected with the theory of vector bundles. Theorems are not always formulated in maximal generality but rather in such a way that the geometric nature of the objects comes to the fore. Whenever possible examples are given to illustrate the role of vector bundles. Audience: With numerous illustrations and applications to various problems in mathematics and the sciences, the book will be of interest to a range of graduate students from pure and applied mathematics.

Koszul Cohomology and Algebraic Geometry

Author : Marian Aprodu
Publisher : American Mathematical Soc.
ISBN 13 : 0821849646
Total Pages : 138 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Koszul Cohomology and Algebraic Geometry by : Marian Aprodu

Download or read book Koszul Cohomology and Algebraic Geometry written by Marian Aprodu and published by American Mathematical Soc.. This book was released on 2010 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Vector Bundles on Complex Projective Spaces

Author : Christian Okonek
Publisher : Springer Science & Business Media
ISBN 13 : 1475714602
Total Pages : 399 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Vector Bundles on Complex Projective Spaces by : Christian Okonek

Download or read book Vector Bundles on Complex Projective Spaces written by Christian Okonek and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = Fn. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some funda mental results from these fields are summarized at the beginning. One of the authors gave a survey in the Seminaire Bourbaki 1978 on the current state of the classification of holomorphic vector bundles overFn. This lecture then served as the basis for a course of lectures in Gottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the introductory nature of this book we have had to leave out some difficult topics such as the restriction theorem of Barth. As compensation we have appended to each sec tion a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of paragraphs. Each section is preceeded by a short description of iv its contents.

Vector Bundles

Author : Andrej N. Tjurin
Publisher : Universitätsverlag Göttingen
ISBN 13 : 3938616741
Total Pages : 330 pages
Book Rating : 4.9/5 (386 download)

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Book Synopsis Vector Bundles by : Andrej N. Tjurin

Download or read book Vector Bundles written by Andrej N. Tjurin and published by Universitätsverlag Göttingen. This book was released on 2008 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a three volume collection of Andrey Nikolaevich Tyurin's Selected Works. It includes his most interesting articles in the field of classical algebraic geometry, written during his whole career from the 1960s. Most of these papers treat different problems of the theory of vector bundles on curves and higher dimensional algebraic varieties, a theory which is central to algebraic geometry and most of its applications.

Syzygies

Author : E. Graham Evans
Publisher : Cambridge University Press
ISBN 13 : 0521314119
Total Pages : 137 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis Syzygies by : E. Graham Evans

Download or read book Syzygies written by E. Graham Evans and published by Cambridge University Press. This book was released on 1985-08-15 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1985 book covers from first principles the theory of Syzygies.

Group Cohomology and Algebraic Cycles

Author : Burt Totaro
Publisher : Cambridge University Press
ISBN 13 : 1107015774
Total Pages : 245 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Group Cohomology and Algebraic Cycles by : Burt Totaro

Download or read book Group Cohomology and Algebraic Cycles written by Burt Totaro and published by Cambridge University Press. This book was released on 2014-06-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

Progress in Commutative Algebra 1

Author : Christopher Francisco
Publisher : Walter de Gruyter
ISBN 13 : 3110250403
Total Pages : 377 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Progress in Commutative Algebra 1 by : Christopher Francisco

Download or read book Progress in Commutative Algebra 1 written by Christopher Francisco and published by Walter de Gruyter. This book was released on 2012-04-26 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.

Lectures on Vector Bundles

Author : J. Le Potier
Publisher : Cambridge University Press
ISBN 13 : 9780521481823
Total Pages : 260 pages
Book Rating : 4.4/5 (818 download)

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Book Synopsis Lectures on Vector Bundles by : J. Le Potier

Download or read book Lectures on Vector Bundles written by J. Le Potier and published by Cambridge University Press. This book was released on 1997-01-28 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work consists of two sections on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, and treats Mumford's geometric invariant theory. The second part centers on the structure of the moduli space of semistable sheaves on the projective plane. The author sketches existence conditions for sheaves of given rank, and Chern class and construction ideas in the general context of projective algebraic surfaces. Professor Le Potier provides a treatment of vector bundles that will be welcomed by experienced algebraic geometers and novices alike.

Commutative Algebra

Author : Irena Peeva
Publisher : Springer Science & Business Media
ISBN 13 : 1461452929
Total Pages : 705 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Commutative Algebra by : Irena Peeva

Download or read book Commutative Algebra written by Irena Peeva and published by Springer Science & Business Media. This book was released on 2013-02-01 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Threading Homology through Algebra

Author : Giandomenico Boffi
Publisher : Clarendon Press
ISBN 13 : 9780191513640
Total Pages : 268 pages
Book Rating : 4.5/5 (136 download)

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Book Synopsis Threading Homology through Algebra by : Giandomenico Boffi

Download or read book Threading Homology through Algebra written by Giandomenico Boffi and published by Clarendon Press. This book was released on 2006-06-29 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Threading Homology through Algebra takes homological themes (Koszul complexes and their variations, resolutions in general) and shows how these affect the perception of certain problems in selected parts of algebra, as well as their success in solving a number of them. The text deals with regular local rings, depth-sensitive complexes, finite free resolutions, letter-place algebra, Schur and Weyl modules, Weyl-Schur complexes and determinantal ideals. Aimed at graduates and academics in mathematics, the book provides an overview of the developments that have taken place in these areas as well as an insight into some of the open problems which exist.

Grassmannians, Moduli Spaces and Vector Bundles

Author : David Ellwood
Publisher : American Mathematical Soc.
ISBN 13 : 0821852051
Total Pages : 190 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Grassmannians, Moduli Spaces and Vector Bundles by : David Ellwood

Download or read book Grassmannians, Moduli Spaces and Vector Bundles written by David Ellwood and published by American Mathematical Soc.. This book was released on 2011 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of cutting-edge articles on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought together a community indebted to the pioneering work of P. E. Newstead, visiting the United States for the first time since the 1960s. Moduli spaces of vector bundles were then in their infancy, but are now, as demonstrated by this volume, a powerful tool in symplectic geometry, number theory, mathematical physics, and algebraic geometry. In fact, the impetus for this volume was to offer a sample of the vital convergence of techniques and fundamental progress, taking place in moduli spaces at the outset of the twenty-first century. This volume contains contributions by J. E. Andersen and N. L. Gammelgaard (Hitchin's projectively flat connection and Toeplitz operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and A. Bertram (stability in higher dimension), L. Jeffrey (intersection cohomology), J. Kamnitzer (Langlands program), M. Lieblich (arithmetic aspects), P. E. Newstead (coherent systems), G. Pareschi and M. Popa (linear series on Abelian varieties), and M. Teixidor i Bigas (bundles over reducible curves). These articles do require a working knowledge of algebraic geometry, symplectic geometry and functional analysis, but should appeal to practitioners in a diversity of fields. No specialization should be necessary to appreciate the contributions, or possibly to be stimulated to work in the various directions opened by these path-blazing ideas; to mention a few, the Langlands program, stability criteria for vector bundles over surfaces and threefolds, linear series over abelian varieties and Brauer groups in relation to arithmetic properties of moduli spaces.

Vector Bundles and Complex Geometry

Author : Oscar García-Prada
Publisher : American Mathematical Soc.
ISBN 13 : 0821858467
Total Pages : 218 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Vector Bundles and Complex Geometry by : Oscar García-Prada

Download or read book Vector Bundles and Complex Geometry written by Oscar García-Prada and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers from the conference on Vector Bundles held at Miraflores de la sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.

The Grassmannian Variety

Author : V. Lakshmibai
Publisher : Springer
ISBN 13 : 1493930826
Total Pages : 172 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis The Grassmannian Variety by : V. Lakshmibai

Download or read book The Grassmannian Variety written by V. Lakshmibai and published by Springer. This book was released on 2015-09-25 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.