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