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

A. L. Knutsen; A. F. Lopez

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

A. L. Knutsen·A. F. Lopez

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Abstract

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]).

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BibTeX RIS

A. L. Knutsen, A. F. Lopez. 2007-06-22. A sharp vanishing theorem for line bundles on K3 or Enriques surfaces. https://arxiv.org/abs/math/0610068

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