Arkiv för Matematik
- Ark. Mat.
- Volume 50, Number 2 (2012), 237-258.
Chern classes of tropical vector bundles
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.
I would like to thank my advisor Andreas Gathmann for numerous helpful discussions.
Ark. Mat., Volume 50, Number 2 (2012), 237-258.
Received: 26 April 2010
Revised: 1 October 2010
First available in Project Euclid: 31 January 2017
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Allermann, Lars. Chern classes of tropical vector bundles. Ark. Mat. 50 (2012), no. 2, 237--258. doi:10.1007/s11512-011-0147-3. https://projecteuclid.org/euclid.afm/1485907175