Borel–Weil factorization for super Grassmannians

• Steven V Sam ^[1]
  1. [1] University of California System

     University of California System

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-026-01131-3
• Enlaces
  • Texto completo
• Resumen

  • This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a free module over the cohomology of the structure sheaf and that the space of generators is an irreducible representation of the general linear supergroup that can be constructed via explicit multilinear operations. Our techniques come from commutative algebra: we relate this cohomology calculation to Tor groups of certain algebraic varieties.

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