Felipe Rincón - Isotropical Linear Spaces and Valuated Delta-Matroids

dmtcs:2954 - Discrete Mathematics & Theoretical Computer Science, January 1, 2011, DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011) - https://doi.org/10.46298/dmtcs.2954
Isotropical Linear Spaces and Valuated Delta-MatroidsConference paper

Authors: Felipe Rincón 1

The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n×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.


Volume: DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)
Section: Proceedings
Published on: January 1, 2011
Imported on: January 31, 2017
Keywords: spinor variety,isotropic subspace,tropical linear space,valuated matroid,delta-matroid,matroid subdivision,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • FRG: Collaborative Research: Semidefinite optimization and convex algebraic geometry; Funder: National Science Foundation; Code: 0757207
  • Computational Algebraic Geometry; Funder: National Science Foundation; Code: 0456960

8 Documents citing this article

Consultation statistics

This page has been seen 256 times.
This article's PDF has been downloaded 463 times.