Ample Line Bundles on Blown Up Surfaces

Details Ample Line Bundles on Blown Up Surfaces Ample Line Bundles on Blown Up Surfaces

1994-10-12

arxiv.org/abs/alg-geom/9410011v1

Mathematics

Algebraic Geometry

4 pages, AMS-TeX 2.1

Scientific paper

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.

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