Chern Numbers of Ample Vector Bundles on Toric Surfaces

Details Chern Numbers of Ample Vector Bundles on Toric Surfaces Chern Numbers of Ample Vector Bundles on Toric Surfaces

1999-11-24

arxiv.org/abs/math/9911192v1

Mathematics

Algebraic Geometry

Latex file, 13 pages

Scientific paper

Let $\sE$ be an ample rank $r$ bundle on a smooth toric projective surface,
$S$, whose topological Euler characteristic is $e(S)$. In this article, we
prove a number of surprisingly strong lower bounds for $c_1(\sE)^2$ and
$c_2(\sE)$. We also enumerate the exceptions to either the inequality
$c_1(\sE)^2\ge 4e(S)$ or the inequality $c_2(\sE)\ge e(S)$ holding.

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