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Algebraic Structures and Moduli Spaces: CRM Workshop, July 14-20, 2003, Montréal, Canada
Edited by: Jacques Hurtubise, McGill University, Montréal, QC, Canada, and Centre de Recherches Mathématiques, Montréal, QC, Canada, and Eyal Markman, University of Massachusetts, Amherst, MA
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Proceedings & Lecture Notes
2004; 258 pp; softcover
Volume: 38
ISBN-10: 0-8218-3568-8
ISBN-13: 978-0-8218-3568-5
List Price: US$87
Member Price: US$69.60
Order Code: CRMP/38
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This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties.

Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kōta Yoshioka, explains their recent work on the moduli space of instantons over \({\mathbb R}^4\).

The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.

Table of Contents

  • M. Lehn -- Lectures on Hilbert schemes
  • H. Nakajima and K. Yoshioka -- Lectures on instanton counting
  • C. Bartocci and M. Jardim -- Hyper-Kähler Nahm transforms
  • A. Braverman -- Instanton counting via affine Lie algebras. I. Equivariant \(J\)-functions of (affine) flag manifolds and Whittaker vectors
  • M. A. A. de Cataldo and L. Migliorini -- The Gysin map is compatible with mixed Hodge structures
  • N.-K. Ho and L. C. Jeffrey -- Representations of fundamental groups of nonorientable 2-manifolds
  • Y. Namikawa -- Mukai flops and derived categories. II
  • S. Hosono, B. H. Lian, K. Oguiso, and S.-T. Yau -- Fourier-Mukai number of a K3 surface
  • J. Sawon -- Derived equivalence of holomorphic symplectic manifolds
  • M. Roth and R. Vakil -- The affine stratification number and the moduli space of curves
  • M. Verbitsky -- Coherent sheaves on generic compact tori
  • W.-P. Li, Z. Qin, and W. Wang -- The cohomology rings of Hilbert schemes via Jack polynomials
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