Toric degenerations of spherical varieties

• Valery Alexeev ^[1] ; Michel Brion ^[2]
  1. [1] University of Georgia

     University of Georgia

     Estados Unidos

     
  2. [2] Institut Fourier

     Institut Fourier

     Arrondissement de Grenoble, Francia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 4, 2005, págs. 453-478
• Idioma: inglés
• DOI: 10.1007/s00029-005-0396-8
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• Resumen

  • We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by mirror symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provide an explanation for the limits as boundary points of the moduli space of stable pairs whose existence is predicted by the Minimal Model Program.