22 citations · 48 across the 8 of their papers we have counts for
11 papers
Stable spherical varieties and their moduli
Valery Alexeev, Michel Brion
We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group and their flat equivariant degenerations. Given any projective…
Classification of log del Pezzo surfaces of index
Valery Alexeev, Viacheslav V. Nikulin
This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we unders…
Toric degenerations of spherical varieties
Valery Alexeev, Michel Brion
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 Symm…
On K-Stability of Reductive Varieties
Valery Alexeev, Ludmil Katzarkov
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don…
Boundedness of spherical Fano varieties
Valery Alexeev, Michel Brion
We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a…
Moduli of affine schemes with reductive group action
Valery Alexeev, Michel Brion
For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, m…