Let X be a smooth projective curve defined on C. The number of holomorphic maps from a fixed X to another curve, (both of genus bigger than or equal to two), is finite by the classical de Franchis theorem. In this paper we get an explicit bound for this number, depending on the genus of X only. Our bound is better than all the previously given ones (by Howard-Sommese and Kani).
Some remarks on the de Franchis theorem / A. Alzati, G.P. Pirola. - In: ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE. - ISSN 0430-3202. - 36:1(1990), pp. 45-52. [10.1007/BF02837205]
Some remarks on the de Franchis theorem
A. AlzatiPrimo
;
1990
Abstract
Let X be a smooth projective curve defined on C. The number of holomorphic maps from a fixed X to another curve, (both of genus bigger than or equal to two), is finite by the classical de Franchis theorem. In this paper we get an explicit bound for this number, depending on the genus of X only. Our bound is better than all the previously given ones (by Howard-Sommese and Kani).
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