Tropical schemes, tropical cycles, and valuated matroids

  • Diane Maclagan

    University of Warwick, Coventry, UK
  • Felipe Rincón

    Queen Mary University of London, UK
Tropical schemes, tropical cycles, and valuated matroids cover
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Abstract

We show that the weights on a tropical variety can be recovered from the tropical scheme structure proposed in [GG16], so there is a well-defined Hilbert–Chow morphism from a tropical scheme to the underlying tropical cycle. For a subscheme of projective space given by a homogeneous ideal II we show that the Giansiracusa tropical scheme structure contains the same information as the set of valuated matroids of the vector spaces IdI_d for d0d ≥ 0. We also give a combinatorial criterion to determine whether a given relation is in the congruence defining the tropical scheme structure.

Cite this article

Diane Maclagan, Felipe Rincón, Tropical schemes, tropical cycles, and valuated matroids. J. Eur. Math. Soc. 22 (2020), no. 3, pp. 777–796

DOI 10.4171/JEMS/932