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October 2012 Chern classes of tropical vector bundles
Lars Allermann
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Ark. Mat. 50(2): 237-258 (October 2012). DOI: 10.1007/s11512-011-0147-3

Abstract

We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Most of the definitions presented here for tropical vector bundles will be contained in Torchiani, C., Line Bundles on Tropical Varieties, Diploma thesis, Technische Universität Kaiserslautern, Kaiserslautern, 2010, for the case of line bundles. Afterwards we use the bounded rational sections of a tropical vector bundle to define the Chern classes of this bundle and prove some basic properties of Chern classes. Finally we give a complete classification of all vector bundles on an elliptic curve up to isomorphisms.

Note

I would like to thank my advisor Andreas Gathmann for numerous helpful discussions.

Citation

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Lars Allermann. "Chern classes of tropical vector bundles." Ark. Mat. 50 (2) 237 - 258, October 2012. https://doi.org/10.1007/s11512-011-0147-3

Information

Received: 26 April 2010; Revised: 1 October 2010; Published: October 2012
First available in Project Euclid: 31 January 2017

zbMATH: 1273.14129
MathSciNet: MR2961320
Digital Object Identifier: 10.1007/s11512-011-0147-3

Rights: 2011 © Institut Mittag-Leffler

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Vol.50 • No. 2 • October 2012
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