Speaker: Marcello Bernardara (Universit Duisburg-Essen) Place: Rm. 206, RIMS, Kyoto University Time: Feb 8, 2011 10:30-12:00. Title: P-stability and moduli spaces on elliptic surfaces Abstract: In a joint work with G. Hein, we use P-stability on the derived category of a smooth elliptic K3 surface to reconstruct moduli spaces of \mu-semistable sheaves with given Mukai vector. This allows to describe the birational maps between different moduli spaces, to determine whether such maps are isomorphisms or Mukai flops, and to show that such moduli spaces have always isomorphic Picard groups.
Speaker: Jan Manschot (CEA Saclay) Place: Rm. 206, RIMS, Kyoto University Date: Jan 18 2011, 10:30 - 12:00 Speaker: Jan Manchot, French Atomic Energy Commission (CEA) Saclay Title: Sheaves on surfaces and generating functions Abstract:The talk will discuss the computation of the generating functions of the Betti numbers of the moduli space of stable sheaves of rank 3 on the projective plane P2 and its blow-up. Wall-crossing is used to obtain the Betti numbers on the blow-up. The Betti numbers for P2 follow from those for the blow-up by the blow-up formula. The generating functions are expressed in terms of modular functions and indefinite theta functions.