Some notes on the moduli of stable sheaves on elliptic surfaces

Abstract

In this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman's results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on ${\Bbb P}^2$ are rational. We also compute the Picard groups of those on Abelian surfaces.