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Moduli Spaces and Arithmetic Geometry (Kyoto, 2004)
Edited by: Shigeru Mukai, Kyoto University, Japan, Yoichi Miyaoka, University of Tokyo, Japan, Shigefumi Mori and Atsushi Moriwaki, Kyoto University, Japan, and Iku Nakamura, Hokkaido University, Sapporo, Japan
A publication of the Mathematical Society of Japan.
cover
Advanced Studies in Pure Mathematics
2007; 432 pp; hardcover
Volume: 45
ISBN-10: 4-931469-38-8
ISBN-13: 978-4-931469-38-9
List Price: US$102
Member Price: US$81.60
Order Code: ASPM/45
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Since its birth, algebraic geometry has been closely related to and deeply motivated by number theory. The modern study of moduli spaces and arithmetic geometry demonstrates that these two areas have many important techniques and ideas in common. With this close relation in mind, the RIMS conference "Moduli Spaces and Arithmetic Geometry" was held at Kyoto University during September 8-15, 2004 as the 13th International Research Institute of the Mathematical Society of Japan.

This volume is the outcome of this conference and consists of thirteen papers by invited speakers, including C. Soulé, A. Beauville and C. Faber, and other participants. All papers, with two exceptions by C. Voisin and Yoshinori Namikawa, treat moduli problem and/or arithmetic geometry. Algebraic curves, Abelian varieties, algebraic vector bundles, connections and D-modules are the subjects of those moduli papers. Arakelov geometry and rigid geometry are studied in arithmetic papers. In the two exceptions, integral Hodge classes on Calabi-Yau threefolds and symplectic resolutions of nilpotent orbits are studied.

Volumes in this series are freely available electronically 5 years post-publication.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and research mathematicians interested in algebra and algebraic geometry.

Table of Contents

  • K. Yoshioka -- Moduli spaces of twisted sheaves on a projective variety
  • D. Huybrechts and P. Stellari -- Appendix. Proof of Caldararu's conjecture
  • C. Voisin -- On integral Hodge classes on uniruled or Calabi-Yau threefolds
  • Y. Namikawa -- Birational geometry of symplectic resolutions of nilpotent orbits
  • T. Abe -- The moduli stack of rank-two Gieseker bundles with fixed determinant on a nodal curve
  • A. Beauville -- Vector bundles on curves and theta functions
  • A. Moriwaki -- On the finiteness of abelian varieties with bounded modular height
  • N. Nitsure -- Moduli of regular holonomic \(\mathcal{D}_X\)-modules with natural parabolic stability
  • I. Nakamura and K. Sugawara -- The cohomology groups of stable quasi-abelian schemes and degenerations associated with the \(E_8\)-lattice
  • C. Soulé -- Semi-stable extensions on arithmetic surfaces
  • C. Consani and C. Faber -- On the cusp form motives in genus 1 and level 1
  • S. Mukai -- Polarized K3 surfaces of genus thirteen
  • K. Fujiwara and F. Kato -- Rigid geometry and applications
  • M. Inaba, K. Iwasaki, and M. Saito -- Moduli of stable parabolic connections, Riemann-Hilbert correspondence and geometry of Painlevé equation of type VI, part II
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