Cohomologies of tautological bundles of matroids

• Christopher Eur ^[1]
  1. [1] Carnegie Mellon University

     Carnegie Mellon University

     City of Pittsburgh, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
• DOI: 10.1007/s00029-024-00979-7
• Enlaces
  • Texto completo
• Resumen

  • Tautological bundles of realizations of matroids were introduced in Berget et al. (Invent Math 233:951–1039, 2023) as a unifying geometric model for studying matroids. We compute the cohomologies of exterior and symmetric powers of these vector bundles, and show that they depend only on the matroid of the realization. As an application, we show that the log canonical bundle of a wonderful compactification of a hyperplane arrangement complement, in particular the moduli space of pointed rational curves M0,n, has vanishing higher cohomologies.

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