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 C×D of two distinct very general curves of genus g>6 and g'>1 does not admit dominant rational maps, other than the identity, on surfaces of general type
Bastianelli, F., Pirola, G. (2013). On dominant rational maps from products of curves to surfaces of general type. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 45(6), 1310-1322 [10.1112/blms/bdt057].
On dominant rational maps from products of curves to surfaces of general type
BASTIANELLI, FRANCESCO;
2013
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 C×D of two distinct very general curves of genus g>6 and g'>1 does not admit dominant rational maps, other than the identity, on surfaces of general type
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