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

2006/10/02 by Andreas Leopold Knutsen, Angelo Felice Lopez, Knutsen, A. L. +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #14C20 #14F17 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Ginseng Biological Effects and Applications

paper · pdf · doi:10.48550/arxiv.math/0610068

openalex publication_date 2006/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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