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Boundedness and $K^2$ for log surfaces
Let $\epsilon, C$ be two positive real numbers, and $\mathcal C \subset \mathbb R$ be a DCC (descending chain condition) set. Let $(X, B = \sum b_j B_j)$ denote a projective surface with an $\mathbbExpand
Complete moduli in the presence of semiabelian group action
I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying aExpand
Compactified Jacobians and Torelli Map
We compare several constructions of compactified jacobians — using semistable sheaves, semistable projective curves, degenerations of abelian varieties, and combinatorics of cell decompositions — andExpand
Two two-dimensional terminations
Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of theExpand
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, weExpand
For a one-dimensiona l family of abelian varieties equipped with principal theta divisors a canonical limit is constructed as a pair consisting of a reduced projective variety and a Cartier divisorExpand
Stable reductive varieties II: projective case
Abstract We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stableExpand
Bounding Singular Surfaces of General Type
We provide simpler proofs of several boundedness theorems, contained in in articles [2], [3], for log surfaces of general type with semi log canonical singularities. At the same time, we make theseExpand
Log canonical singularities and complete moduli of stable pairs
1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stableExpand