Wallcrossing for Ktheoretic Donaldson invariants and computations for rational surfaces
Wallcrossing for Ktheoretic Donaldson invariants and computations for rational surfaces

Lothar Goettsche, International Centre for Theoretical Physics (ICTP)
Fine Hall 322
Let $(X,H)$ be a polarized algebraic surface. Let $M=M^H_X(c_1,c_2)$ be the moduli spaces of $H$semistable rank 2 sheaves on $X$ with Chern classes $c_1, c_2$. Ktheoretic Donaldson invariants of $X$ are holomorphic Euler characteristics of determinant line bundles on $M$. These invariants are subject to wallcrossing when $H$ varies. In the first part of the lecture I present joint work with Nakajima and Yoshioka, where we determine a generating function for the wallcrossing in terms of elliptic functions. If time permits I will in the second part of the talk present some results about the Ktheoretic invariants of rational surfaces, and relate these to Le Potiers strange duality conjecture.