Isotropical Linear Spaces and Valuated Delta-Matroids
Combinatorics
2013-03-07 v1 Algebraic Geometry
Abstract
The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n x n skew-symmetric matrix. Its points correspond to n-dimensional isotropic subspaces of a 2n-dimensional vector space. In this paper we tropicalize this picture, and we develop a combinatorial theory of tropical Wick vectors and tropical linear spaces that are tropically isotropic. We characterize tropical Wick vectors in terms of subdivisions of Delta-matroid polytopes, and we examine to what extent the Wick relations form a tropical basis. Our theory generalizes several results for tropical linear spaces and valuated matroids to the class of Coxeter matroids of type D.
Keywords
Cite
@article{arxiv.1004.4950,
title = {Isotropical Linear Spaces and Valuated Delta-Matroids},
author = {Felipe Rincón},
journal= {arXiv preprint arXiv:1004.4950},
year = {2013}
}