I prove the existence, and describe the structure, of moduli space of pairs (P, Î˜) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying aâ€¦ (More)

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 giveâ€¦ (More)

Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see [KMM] for introduction. In [SH2] it was conjectured that many of the interesting sets,â€¦ (More)

The space of subvarieties of P n with a fixed Hilbert polynomial is not complete. Grothendieck defined a completion by relaxing " variety " to " scheme " , giving the complete Hilbert scheme ofâ€¦ (More)

We compare several constructions of compactified jacobians using semistable sheaves, semistable projective curves, degenerations of abelian varieties, and combinatorics of cell decompositions andâ€¦ (More)

This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities (equivalently, quotient singularities) of index â‰¤ 2. Byâ€¦ (More)

Definition 0-i. Let X be a normal complex variety of dimension n, A = ~ b E a divisor with rational coefficients b such that O<-b <I, l i i i E I simple Weil divisors on X. Then X is said to haveâ€¦ (More)

0.1. This paper consists of two parts. In the first part, assuming the log Minimal Model Program (which is currently only known to be true in dim â‰¤ 3), we construct the complete moduli of â€œstableâ€¦ (More)

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, multiplicity-finiteâ€¦ (More)