Chern Numbers of Ample Vector Bundles on Toric Surfaces

Sandra Di Rocco; Andrew J. Sommese

Chern Numbers of Ample Vector Bundles on Toric Surfaces

Algebraic Geometry 2007-05-23 v1

Authors: Sandra Di Rocco , Andrew J. Sommese

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.

Keywords

vector bundles moduli spaces of vector bundles nef and ample line bundles

Cite

@article{arxiv.math/9911192,
  title  = {Chern Numbers of Ample Vector Bundles on Toric Surfaces},
  author = {Sandra Di Rocco and Andrew J. Sommese},
  journal= {arXiv preprint arXiv:math/9911192},
  year   = {2007}
}

Comments

Latex file, 13 pages

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