English

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

Algebraic Geometry 2007-06-22 v2

Abstract

Let LL be a line bundle on a K3 or Enriques surface. We give a vanishing theorem for H1(L)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]).

Keywords

Cite

@article{arxiv.math/0610068,
  title  = {A sharp vanishing theorem for line bundles on K3 or Enriques surfaces},
  author = {A. L. Knutsen and A. F. Lopez},
  journal= {arXiv preprint arXiv:math/0610068},
  year   = {2007}
}

Comments

4 pages, latex. Minor corrections. To appear on Proc. Amer. Math. Soc

R2 v1 2026-07-22T17:43:26.706Z