Compact moduli spaces and vector bundles : conference on compact moduli and vector bundles, October 21-24, 2010, University of Georgia, Athens, Georgia / Valery Alexeev [and four others], editors.

Format:

Book

Contributor:

Alexeev, Valery, 1964- editor.

Series:

Contemporary mathematics, 0271-4132 564

Contemporary mathematics, 564 0271-4132

Language:

English

Subjects (All):

Vector bundles--Congresses.

Vector bundles.

Moduli theory--Congresses.

Moduli theory.

Physical Description:

1 online resource (264 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

This book contains the proceedings of the conference on Compact Moduli and Vector Bundles, held from October 21-24, 2010, at the University of Georgia. This book is a mix of survey papers and original research articles on two related subjects: Compact Moduli spaces of algebraic varieties, including of higher-dimensional stable varieties and pairs, and Vector Bundles on such compact moduli spaces, including the conformal block bundles. These bundles originated in the 1970s in physics; the celebrated Verlinde formula computes their ranks. Among the surveys are those that examine compact moduli spaces of surfaces of general type and others that concern the GIT constructions of log canonical models of moduli of stable curves. The original research articles include, among others, papers on a formula for the Chern classes of conformal classes of conformal block bundles on the moduli spaces of stable curves, on Looijenga's conjectures, on algebraic and tropical Brill-Noether theory, on Green's conjecture, on rigid curves on moduli of curves, and on Steiner surfaces.

Contents:

Preface

Talks at the UGA conference

Compact moduli spaces of surfaces of general type

1. Introduction

2. Moduli of stable surfaces

3. Infinitesimal study of the moduli stack

4. Wahl singularities

5. Orbifold double normal crossing singularities

6. Surfaces with boundary

7. Plane curves

8. Exceptional vector bundles associated to degenerations of surfaces

9. Boundary divisors of the moduli space of stable surfaces

10. Relation with Donaldson theory

11. Other examples of boundary divisors

References

Rigid curves on \{ }_{0, } and arithmetic breaks

2. The Keel-M\textsuperscript{c}Kernan theorem

3. Surfaces in \ { }_{0, } from configurations of points in â??²

4. The hypergraph construction

5. The dual Hesse configuration and a rigid curve on \ { }_{0,12}

6. The "Two Conics" construction

7. Arithmetic break of a hypergraph curve

8. Rigid matroids

9. Arithmetic break of a "Two Conics" curve - part I

10. Arithmetic break of a "Two Conics" curve - part II

Algebraic and combinatorial Brill-Noether theory

2. Algebro-geometric preliminaries

3. Divisor theory on graphs

4. Baker specialization lemma refined

5. Specialization for graphs with loops

6. On the emptyness of Brill-Noether loci

GIT constructions of log canonical models of \ { }_{ }

2. Parameter spaces

3. Finite Hilbert Stability

4. Unstable curves: Degenerate and non-reduced curves

5. Unstable curves: Badly singular curves and special subcurves

6. Local study of the moduli spaces of c-semistable and of h-semistable curves

The geometry of the ball quotient model of the moduli space of genus four curves

Introduction

1. Preliminaries on canonical genus 4 curves and cubic 3-folds

2. GIT for =4 curves via cubic 3-folds

3. Stability for canonical genus 4 curves

4. Hassett"Keel Program

5. Ball quotient model for the moduli of genus 4 curves

6. The comparison of the GIT and ball quotient models

Two remarks on the Weierstrass flag

2. Linear series of Weierstrass type

3. On the Weierstrass flags

Chern classes of conformal blocks

2. Conformal blocks

3. The case =0

4. =0, = â??

5. =0, arbitrary and â??=1

6. The case >0

7. Questions

Restrictions of stable bundles

Orthogonal bundles, theta characteristics and symplectic strange duality

2. Moduli spaces

3. Hitchin's connection and the geometric Segal-Sugawara tensor

4. The proof of Proposition 2.2

References.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8537-5