Total positivity for matroid Schubert varieties

• Xuhua He ^[1] ; Connor Simpson ^[2] ; Kaitao Xie ^[1]
  1. [1] University of Hong Kong

     University of Hong Kong

     RAE de Hong Kong (China)

     
  2. [2] Institute for Advanced Study

     Institute for Advanced Study

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01080-3
• Enlaces
  • Texto completo
• Resumen

  • We define the totally nonnegative matroid Schubert variety Y_V of a linear subspace V ⊂ R^n. We show that Y_V is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats of the oriented matroid of V. This closely resembles the regularity theorem for totally nonnegative generalized flag varieties. As a corollary, we obtain a regular CW structure on the real matroid Schubert variety of V.

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