edited by Shigeru Mukai (RIMS, Kyoto University, Japan) , Shigefumi Mori (RIMS, Kyoto University, Japan) , Yoichi Miyaoka (University of Tokyo, Japan) , Atsushi Moriwaki (Kyoto University, Japan) , & Iku Nakamura (Hokkaido University, Japan)

Since its birth algebraic geometry has been closely related to and deeply motivated by number theory. Particularly the modern study of moduli spaces and arithmetic geometry 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 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.

Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

• Moduli Spaces of Twisted Sheaves on a Projective Variety (K Yoshioka)
• Appendix: Proof of C.ald.araru's Conjecture (D Huybrechts & P Stellari)
• On Integral Hodge Classes on Uniruled or Calabi-Yau Threefolds (C Voisin)
• Birational Geometry of Symplectic Resolutions of Nilpotent Orbits (Y Namikawa)
• The Moduli Stack of Rank-two Gieseker Bundles with Fixed Determinant on a Nodal Curve (T Abe)
• Vector Bundles on Curves and Theta Functions (A Beauville)
• On the Finiteness of Abelian Varieties with Bounded Modular Height (A Moriwaki)
• Moduli of Regular HolonomicD_X-modules with Natural Parabolic Stability (N Nitsure)
• The Cohomology Groups of Stable Quasi-abelian Schemes and Degenerations Associated with the E₈-lattice (I Nakamura & K Sugawara)
• Semi-stable Extensions on Arithmetic Surfaces (C Soulé)
• On the Cusp FormMotives in Genus 1 and Level 1 (C Consani & C Faber)
• Polarized K3 Surfaces of Genus Thirteen (S Mukai)
• Rigid Geometry and Applications (K Fujiwara & F Kato)
• Moduli of Stable Parabolic Connections, Riemann-Hilbert Correspondence and Geometry of Painlevé Equation of Type VI, Part II (M Inaba, K Iwasaki & M Saito)