The partial compactification of the universal centralizer

• Ana Bălibanu ^[1]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 5, 2023
• Idioma: inglés
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• Resumen

  • The universal centralizer of a semisimple algebraic group G is the family of centralizers of regular elements, parametrized by their conjugacy classes. When G is of adjoint type, we construct a smooth, log-symplectic fiberwise compactification Z of the universal centralizer Z by taking the closure of each fiber in the wonderful compactification G. We use the geometry of the wonderful compactification to give an explicit description of the symplectic leaves of Z. We also show that its compactified centralizer fibers are isomorphic to certain Hessenberg varieties—we apply this connection to compute the singular cohomology of Z, and to study the geometry of the corresponding universal Hessenberg family.