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Some remarks on the de Franchis theorem

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Summary

LetX be a smooth projective curve defined onC. The number of holomorphic maps from a fixedX 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 ofX only. Our bound is better than all the previously given ones (by Howard-Sommese and Kani).

Sommario

SiaX una curva liscia proiettiva definita suC. Il numero delle applicazioni olomorfe esistenti tra unaX fissata ed un'altra curva, (entrambe di genere maggiore od uguale a due), è finito in base al classico teorema di de Franchis. In questo lavoro noi otteniamo, per tale numero, un limite superiore esplicito, dipendente solo dal genere diX. La nostra stima è migliore di tutte quelle date precedentemente (da Howard-Sommese e da Kani).

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References

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Author notes

  1. A. Alzati (member of the G.N.S.A.G.A. of the italian C.N.R.)

    Present address: Dip. di Mat., Univ. di Milano, via C. Saldini 50, 20133, Milano

  2. G. P. Pirola (member of the G.N.S.A.G.A. of the italian C.N.R.)

    Present address: Dip. di Mat., Univ. di Pavia, via Strada Nuova 65, 27100, Pavia

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    1. A. Alzati
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    2. G. P. Pirola
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    Alzati, A., Pirola, G.P. Some remarks on the de Franchis theorem. Ann. Univ. Ferrara 36, 45–52 (1990). https://doi.org/10.1007/BF02837205

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    • DOI: https://doi.org/10.1007/BF02837205

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