2004/03/23 by Valery Alexeev, Alexeev, Valery, Michel Brion +1 · 1 citation
Mathematics · #14M17 #14M25 #20G20 #52B20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT) #math.AG #math.RT #msc:14M17 #msc:14M25 #msc:20G20 #msc:52B20
paper · pdf · doi:10.48550/arxiv.math/0403379
22 pages, 1 figure
arxiv created 2004/03/23 · openalex publication_date 2004/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.