On a conjecture of Beltrametti and Sommese

Andreas Höring

On a conjecture of Beltrametti and Sommese

Algebraic Geometry 2017-12-06 v3

Authors: Andreas Höring

Abstract

Let X be a projective manifold of dimension n. Beltrametti and Sommese conjectured that if A is an ample divisor such that $K_X+(n-1)A$ is nef, then $K_X+(n-1)A$ has non-zero global sections. We prove a weak version of this conjecture in arbitrary dimension. In dimension three, we prove the stronger non-vanishing conjecture of Ambro, Ionescu and Kawamata and give an application to Seshadri constants.

Keywords

projective manifold ample divisor nef divisor non-vanishing conjecture Seshadri constant algebraic geometry

Cite

@article{arxiv.0912.1295,
  title  = {On a conjecture of Beltrametti and Sommese},
  author = {Andreas Höring},
  journal= {arXiv preprint arXiv:0912.1295},
  year   = {2017}
}

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