Vector bundles in algebraic geometry : Durham, 1993 / edited by N.J. Hitchin, P.E. Newstead, W.M. Oxbury.

Format:

Book

Conference/Event

Contributor:

Hitchin, N. J. (Nigel J.), 1946- editor.

Newstead, P. E., editor.

Oxbury, W. M., editor.

Conference Name:

LMS Durham Symposium (1993)

Series:

London Mathematical Society lecture note series ; 208.

London Mathematical Society lecture note series ; 208

Language:

English

Subjects (All):

Vector bundles--Congresses.

Vector bundles.

Physical Description:

1 online resource (ix, 345 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1995.

Language Note:

English

Summary:

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 of the leading researchers in the field to explore further these interactions. This book is a collection of survey articles by the main speakers at the symposium and presents to the mathematical world an overview of the key areas of research involving vector bundles. Topics covered include those linking gauge theory and geometric invariant theory such as augmented bundles and coherent systems; Donaldson invariants of algebraic surfaces; Floer homology and quantum cohomology; conformal field theory and the moduli spaces of bundles on curves; the Horrocks-Mumford bundle and codimension 2 subvarieties in P4 and P5; exceptional bundles and stable sheaves on projective space.

Contents:

Cover; Title; Copyright; Contents; List of participants; Introduction; On the deformation theory of moduli spaces of vector bundles; 0 Introduction; 1 Deformations of the moduli space; 2 Intermediate Jacobians, Torelli-type theorems; 3 Deformations of the Picard bundle; References; Stable augmented bundles over Riemann surfaces; Introduction; 1. Stability for Augmented Bundles; 2. Analytic Aspects; 3. The Stability Parameters; 4. Moduli spaces; 5. Master spaces; 6.Other Augmented Bundles; References; On surfaces in P4 and 3-folds in P5; 0. INTRODUCTION; 1. CONSTRUCTIONS VIA SYZYGIES

2. LIAISON3. ADJUNCTION THEORY; 4. SURFACES IN P4; 5. 3-FOLDS IN P5; 6. EXAMPLES: TWO FAMILIES OF BIRATIONAL CALABI-YAU 3-FOLDS IN P5; 7. OVERVIEW; REFERENCES; Exceptional bundles and moduli spaces of stable sheaves on Pn; 1 Introduction; 2 Logarithmic invariants; 3 Exceptional bundles; 4 The geometry associated to exceptional bundles; 5 Existence theorems; 6 Descriptions of moduli spaces of semi-stable sheaves using exceptional bundles; References; Floer homology and algebraic geometry; 1. INTRODUCTION; 2. FLOER HOMOLOGY AND THE FUKAYA-FLOER THEORY; 3. ELLIPTIC SURFACES

4. CURVES OF HIGHER GENUS AND QUANTUM COHOMOLOGYREFERENCES; The Horrocks-Mumford bundle; I Vector bundles on Pn; II Construction methods for the Horrocks-Mumford bundle; Ill First geometric properties of F; IV Classification of HM-surfaces; V The Horrocks-Mumford bundle and abelian surfaces; References; Faisceaux semi-stables et systèmes cohérents; Introduction; 1. L'espace de modules de Simpson; 2. Fibrés déterminants sur Mx(c); 3. Faisceaux semi-stables sur le plan projectif; 4. Systèmes cohérents; 5. Exemples et applications; Bibliographie; The combinatorics of the Verlinde formulas

1. INTRODUCTION2. TOPOLOGICAL FIELD THEORY AND FUSION ALGEBRAS; 3. RESIDUE FORMULAS; 4. MULTIPLE ζ-VALUES AND INTERSECTION NUMBERS OF MODULI SPACES; REFERENCES; Canonical and almost canonical spin polynomials of an algebraic surface; 0. INTRODUCTION; 1. JACOBIAN OF A SURFACE; 2. JUMPING FILTRATION AND SPIN POLYNOMIALS; 3. SPACES OF JUMPING INSTANTONS; 4. FIRST STEP OF GAP; 5. BEGINNING OF THE CORRECTING PROCEDURE: CROSSES; 6. PARTIAL MODIFICATION AND REGULARISATION; REFERENCES; On conformal field theory; Introduction; Chapter I Conformal Field Theory with Gauge Symmetries

Chapter II Abelian Conformal Field TheoryREFERENCES

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references.

ISBN:

1-139-88519-7

1-107-36715-8

1-107-37177-5

1-107-36224-5

1-107-36855-3

1-299-40484-7

1-107-36469-8

0-511-56931-9