Toric degenerations of spherical varieties

Abstract

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.

22 pages, 1 figure

References in corpus (4)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Log canonical singularities and complete moduli of stable pairs
• SAGBI bases and Degeneration of Spherical Varieties to Toric Varieties
• Adapted algebras and standard monomials

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• Continuous crystals and Duistermaat-Heckman measure for Coxeter groups
• Note on cohomology rings of spherical varieties and volume polynomial
• Monodromy calculatons of fourth order equations of Calabi-Yau type
• The $m-$dissimilarity map and representation theory of $S{L}_m$
• Toric degenerations of weight varieties and applications
• The Gromov width of coadjoint orbits of the symplectic group
• Compactifications of character varieties and skein relations on conformal blocks
• Birational sequences and the tropical Grassmannian
• Standard monomial theory for wonderful varieties
• Toric Degenerations of GIT Quotients, Chow Quotients, and $\bar{M_{0,n}$
• Toric symplectic singular spaces I: isolated singularities