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Chern Numbers of Ample Vector Bundles on Toric Surfaces

Sandra Di Rocco·Andrew J. Sommese
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Abstract

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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Sandra Di Rocco, Andrew J. Sommese. 1999-11-24. Chern Numbers of Ample Vector Bundles on Toric Surfaces. https://arxiv.org/abs/math/9911192

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