A sharp vanishing theorem for line bundles on K3 or Enriques surfaces

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Let $L$ be a line bundle on a K3 or Enriques surface. We give a vanishing theorem for $H^1(L)$ that, unlike most vanishing theorems, gives necessary and sufficient geometrical conditions for the vanishing. This result is essential in our study of Brill-Noether theory of curves on Enriques surfaces (reference [KL1]) and of Enriques-Fano threefolds (reference [KLM]).
4 pages, latex. Minor corrections. To appear on Proc. Amer. Math. Soc

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Algebraic Geometry, 14F17, 14J28, 14C20

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http://salesiana.dossiersoluciones.com/handle/123456789/132202

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610068
 http://arxiv.org/abs/math/0610068

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arXiv