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

TL;DR

This paper proves that products of two very general curves of genus greater than 6 and 1 do not admit dominant rational maps to other surfaces of general type, highlighting restrictions on such mappings.

Contribution

It establishes a non-existence result for dominant rational maps from certain products of curves to surfaces of general type, extending understanding of their geometric properties.

Findings

No dominant rational maps from CxD to other surfaces of general type for specified genera.

Restrictions on mappings depend on the genera of the curves involved.

Results apply to very general curves with genus g>6 and g'>1.

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.