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arXiv:math/0610068 [math.AG]AbstractReferencesReviewsResources

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

A. L. Knutsen, A. F. Lopez

Published 2006-10-02, updated 2007-06-22Version 2

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]).

Comments: 4 pages, latex. Minor corrections. To appear on Proc. Amer. Math. Soc
Categories: math.AG
Subjects: 14F17, 14J28, 14C20
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