Ample Line Bundles on Blown Up Surfaces

Oliver Küchle

Ample Line Bundles on Blown Up Surfaces

alg-geom 2008-02-03 v1 Algebraic Geometry

Authors: Oliver Küchle

Abstract

Given a smooth complex projective surface $S$ and an ample divisor $H$ on $S$ , consider the blow up of $S$ along $k$ points in general position. Let $H'$ be the pullback of $H$ and $E_1,..., E_k$ be the exceptional divisors. We show that $L = nH' -E_1 - ... -E_k$ is ample if and only if $L^2$ is positive provided the integer $n$ is at least 3.

Keywords

blow-up incidence geometry of points and lines

Cite

@article{arxiv.alg-geom/9410011,
  title  = {Ample Line Bundles on Blown Up Surfaces},
  author = {Oliver Küchle},
  journal= {arXiv preprint arXiv:alg-geom/9410011},
  year   = {2008}
}

Comments

4 pages, AMS-TeX 2.1

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