On dominant rational maps from products of curves to surfaces of general type

Abstract

In this paper we investigate the existence of generically finite dominant rational maps from products of curves to surfaces of general type. We prove that the product CxD of two distinct very general curves of genus g>6 and g'>1 does not admit dominant rational maps on other surfaces of general type.

arXiv comment13 pages, minor changes, to appear on Bull. Lond. Math. Soc