Chern classes of tropical vector bundles

Lars Allermann Fachbereich Mathematik, Technische Universit├Ąt Kaiserslautern

Differential Geometry mathscidoc:1701.01016

Arkiv for Matematik, 50, (2), 237-258, 2010.4
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 Universit├Ąt 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.
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@inproceedings{lars2010chern,
  title={Chern classes of tropical vector bundles},
  author={Lars Allermann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632864315023},
  booktitle={Arkiv for Matematik},
  volume={50},
  number={2},
  pages={237-258},
  year={2010},
}
Lars Allermann. Chern classes of tropical vector bundles. 2010. Vol. 50. In Arkiv for Matematik. pp.237-258. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203632864315023.
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