Compact Moduli Spaces and Vector Bundles
About this Title
Valery Alexeev, University of Georgia, Athens, GA, Angela Gibney, University of Georgia, Athens, GA, Elham Izadi, University of Georgia, Athens, GA, János Kollár, Princeton University, Princeton, NJ and Eduard Looijenga, Universiteit Utrecht, Utrecht, The Netherlands, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 564
ISBNs: 978-0-8218-6899-7 (print); 978-0-8218-8537-6 (online)
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.
Graduate students and research mathematicians interested in algebraic geometry and moduli theory.
Table of Contents
- Paul Hacking – Compact moduli spaces of surfaces of general type
- Ana-Maria Castravet and Jenia Tevelev – Rigid curves on and arithmetic breaks
- Lucia Caporaso – Algebraic and combinatorial Brill-Noether theory
- Jarod Alper and Donghoon Hyeon – GIT constructions of log canonical models of
- Sebastian Casalaina-Martin, David Jensen and Radu Laza – The geometry of the ball quotient model of the moduli space of genus four curves
- Enrico Arbarello and Gabriele Mondello – Two remarks on the Weierstrass flag
- Najmuddin Fakhruddin – Chern classes of conformal blocks
- V. Balaji and János Kollár – Restrictions of stable bundles
- Prakash Belkale – Orthogonal bundles, theta characteristics and symplectic strange duality
- Sándor J. Kovács – The splitting principle and singularities
- Shigeru Mukai – Igusa quartic and Steiner surfaces
- Marian Aprodu and Gavril Farkas – Green's conjecture for general covers
- Brendan Hassett and Yuri Tschinkel – Spaces of sections of quadric surface fibrations over curves