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Algebraic Surfaces and Holomorphic Vector Bundles
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Robert Friedman
This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first year course in algebraic geometry (at the level of Hartshorne's ALGEBRAIC GEOMETRY), as well as more advanced graduate students and researchers in the areas of algebraic geometry, ...
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Complex Projective Geometry: Selected Papers
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G Ellingsrud (Editor), C Peskine (Editor), S A Stromme (Editor)
Algebraic geometers have renewed their interest in the interplay between algebraic vector bundles and projective embeddings. New methods have been developed for questions such as: what is the geometric content of syzygies and of bundles derived from them? how can they be used for giving good compactifications of natural families? which ...
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Isomonodromic Deformations and Frobenius Manifolds: An Introduction
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Claude Sabbah
The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and ...
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Moduli of Vector Bundles
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Masaki Maruyama (Editor), Maruyama Maruyama
Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry.
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Categories, Bundles and Spacetime Topology
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C T J Dodson
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Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor D-Modules
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Takuro Mochizuki
The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat ...
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Vector Bundles in Algebraic Geometry
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N J Hitchin (Editor), W M Oxbury (Editor), P E Newstead (Editor)
The study of vector bundles over algebraic varieties has been stimulated over the last few years by successive waves of migrant concepts, largely from mathematical physics, whilst retaining its roots in old questions concerning subvarieties of projective space. The 1993 Durham Symposium on Vector Bundles in Algebraic Geometry brought together some ...
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Schubert Varieties and Degeneracy Loci
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Mr. William Fulton, Piotr Pragacz
Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, taken from a summer school in Thurnau, aim to give an introduction to these topics, and to describe late-1990s progress on these problems. There are interesting interactions with the algebra of ...
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Vector Bundles and Representation Theory: Conference on Hilbert Schemes, Vector Bundles, and Their Interplay with Representation Theory, April 5-7, 2002, University of Missouri, Columbia
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by
Steven Dale Cutkosky
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 ...
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Algebraic Cycles, Sheaves, Shtukas, and Moduli: Impanga Lecture Notes
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by
Piotr Pragacz (Editor)
The articles in this volume are devoted to:moduli of coherent sheaves; principal bundles and sheaves and their moduli; new insights into Geometric Invariant Theory; stacks of shtukas and their compactifications; algebraic cycles vs. commutative algebra; Thom polynomials of singularities; zero schemes of sections of vector bundles. The main purpose ...
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Lectures on Vector Bundles
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Joseph Le Potier, Bela Bollobas (Editor), W Fulton (Editor)
This work consists of two courses on the moduli spaces of vector bundles. The first part tackles the classification of vector bundles on algebraic curves. The construction and elementary properties of the moduli spaces of stable bundles are also discussed. In particular, Hilbert-Grothendieck schemes of vector bundles are constructed, and Mumford's ...
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Holomorphic Vector Bundles Over Compact Complex Surfaces
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Vasile Brinzanescu
The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector ...
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Helices and vector bundles Seminaire Rudakov
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by
Rudakov
This volume is devoted to the use of helices as a method for studying exceptional vector bundles, an important and natural concept in algebraic geometry. The work arises out of a series of seminars organised in Moscow by A. N. Rudakov. The first article sets up the general machinery, and later ones explore its use in various contexts. As to be ...
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Vector Bundles on Curves - New Directions
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by
Shrawan Kumar, Gerard Laumon, Ulrich Stuhler
Giving a survey of some recent developments in the theory of bundles on curves, this text deals with: the relation between conformal blocks and generalized theta functions; Drinfeld Shtukas; and Drinfeld modules and Elliptic Sheaves.
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Vector Bundles and Their Applications
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by
Glenys Luke, Aleksandra S Mishchenko, Alexander S Mishchenko
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 ...
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Cohomology of Vector Bundles and Syzygies
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Jerzy Weyman, Bela Bollobas (Editor), W Fulton (Editor)
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 ...
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Vector Fields and Other Vector Bundle Morphisms: A Singularity Approach
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U Koschorke
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Vector Bundles in Mathematical Physics
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by
Robert Hermann
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Holomorphic Vector Fields on Compact Kahler Manifolds
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by
Yozo Matsushima
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Noether-Lefschetz Problems for Degeneracy Loci
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by
J Spandaw
In this monograph, we study the cohomology of degeneracy loci of the following type. Let $X$ be a complex projective manifold of dimension $n$, let $E$ and $F$ be holomorphic vector bundles on $X$ of rank $e$ and $f$, respectively, and let $\psi\colon F\to E$ be a holomorphic homomorphism of vector bundles. Consider the degeneracy locus $Z:=D_r( ...
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Vanishing Theorems on Complex Manifolds
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by
Bernard Shiffman
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Differential geometry of complex vector bundles
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Kobayashi
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Singularities, representation of algebras, and vector bundles proceedings of a symposium held in Lambrecht / Pfalz ... 1985
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by
Greuel, Trautmann
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction. These relations however cannot be considered to be either completely understood or fully ...
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Moduli Spaces and Vector Bundles
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by
Leticia Brambila-Paz (Editor), Steven B Bradlow (Editor), Oscar Garcia-Prada (Editor)
Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. In recent decades this subject has been greatly enhanced by its relationships with other areas of mathematics, including differential geometry, topology and even theoretical physics, specifically gauge theory, quantum field theory and string ...
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Complex Algebraic Varieties
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by
Klaus Hulek (Editor), Thomas Peternell (Editor), Michael Schneider (Editor)
The Bayreuth meeting on "Complex Algebraic Varieties" focused on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference.
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