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Algebraic, tropical, and fuzzy geometry

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Abstract

The relatively new field of “Tropical Geometry” and “Classical Algebraic Geometry” have much in common. In this paper, we present a unified approach to both of these fields by studying more general “Fuzzy Geometries” over fuzzy rings. It turns out that the fuzzy ring which underlies “Tropical Geometry” is the same as that belonging to “Valuated Matroids”.

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Author information

Authors and Affiliations

  1. Department for Combinatorics and Geometry, CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, 320 Yue Yang Road, Shanghai, China

    Andreas Dress

  2. Institute of Mathematics, University of Leipzig, Postfach 10 09 20, 04009, Leipzig, Germany

    Walter Wenzel

  3. Institute of Mathematics, University of Kassel, 34109, Kassel, Germany

    Walter Wenzel

Authors
  1. Andreas Dress
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  2. Walter Wenzel
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Corresponding author

Correspondence to Walter Wenzel.

Additional information

This research was supported in part by MPI for Mathematics in the Sciences.

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Dress, A., Wenzel, W. Algebraic, tropical, and fuzzy geometry. Beitr Algebra Geom 52, 431–461 (2011). https://doi.org/10.1007/s13366-011-0017-y

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  • DOI: https://doi.org/10.1007/s13366-011-0017-y

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