334 research outputs found

    Decisiones sacri Regii Consilii Neapolitani

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    Marca tip. en port[flor]\p4\s, A-Z\p8\s, 2A-2B\p8\s, a-f\p8\s, g-h\p6\

    Some remarks on the de Franchis theorem

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    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)

    Strong generic vanishing and a higher dimensional Calstelnuovo-de Franchis inequality

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    We extend to manifolds of arbitrary dimension the Castelnuovo-de Franchis inequality for surfaces. The proof is based on the theory of Generic Vanishing and higher regularity, and on the Evans-Griffith Syzygy Theorem in commutative algebra. Along the way we give a positive answer, in the setting of Kahler manifolds, to a question of Green-Lazarsfeld on the vanishing of higher direct images of Poincare' bundles. We indicate generalizations to arbitrary Fourier-Mukai transforms
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