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Transactions of the American Mathematical Society

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Chern numbers of ample vector bundles on toric surfaces


Authors: Sandra Di Rocco and Andrew J. Sommese
Journal: Trans. Amer. Math. Soc. 356 (2004), 587-598
MSC (2000): Primary 14J60, 14M25; Secondary 14J25
DOI: https://doi.org/10.1090/S0002-9947-03-03431-7
Published electronically: September 22, 2003
MathSciNet review: 2022712
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Abstract: This article shows a number of strong inequalities that hold for the Chern numbers $c_1^2$, $c_2$ of any ample vector bundle $\mathcal{E}$ of rank $r$ on a smooth toric projective surface, $S$, whose topological Euler characteristic is $e(S)$. One general lower bound for $c_1^2$ proven in this article has leading term $(4r+2)e(S)\ln_2\left(\tfrac{e(S)}{12}\right)$. Using Bogomolov instability, strong lower bounds for $c_2$ are also given. Using the new inequalities, the exceptions to the lower bounds $c_1^2> 4e(S)$ and $c_2>e(S)$ are classified.


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Additional Information

Sandra Di Rocco
Affiliation: Department of Mathematics, KTH, S-100 44 Stockholm, Sweden
Email: sandra@math.kth.se

Andrew J. Sommese
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: sommese@nd.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03431-7
Keywords: Toric variety, ample vector bundles, Chern numbers
Received by editor(s): March 10, 2001
Received by editor(s) in revised form: April 17, 2002
Published electronically: September 22, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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