English

Toric degenerations of spherical varieties

Algebraic Geometry 2007-05-23 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.math/0403379,
  title  = {Toric degenerations of spherical varieties},
  author = {Valery Alexeev and Michel Brion},
  journal= {arXiv preprint arXiv:math/0403379},
  year   = {2007}
}

Comments

22 pages, 1 figure

R2 v1 2026-07-22T17:03:38.143Z