Author
V V Shokurov
Other affiliations: Russian Academy of Sciences
Bio: V V Shokurov is an academic researcher from Johns Hopkins University. The author has contributed to research in topics: Function field of an algebraic variety & Algebraic cycle. The author has an hindex of 11, co-authored 24 publications receiving 794 citations. Previous affiliations of V V Shokurov include Russian Academy of Sciences.
Papers
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TL;DR: In this article, it was shown that 3-fold log flips exist for log canonical and -factorial log terminal models, as well as a positive answer to the inversion problem for logcanonical and log terminal adjunction.
Abstract: We prove that 3-fold log flips exist. We deduce the existence of log canonical and -factorial log terminal models, as well as a positive answer to the inversion problem for log canonical and log terminal adjunction.
301 citations
TL;DR: In this article, the boundedness of complements modulo two conjectures, Borisov-Alexeev conjecture and effective adjunction for fibre spaces, was proved and proved in two particular cases.
Abstract: We prove the boundedness of complements modulo two conjectures: Borisov–Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.
190 citations
TL;DR: The main result of as mentioned in this paper is a nonvanishing theorem that is a sufficient condition for nontriviality of the zeroth cohomology group of inverse sheaves and applications of this theorem to multidimensional projective geometry are indicated and problems illuminating further insight into the theory of extremal rays are formulated.
Abstract: The main result of the paper is a nonvanishing theorem that is a sufficient condition for nontriviality of the zeroth cohomology group of inverse sheaves. In addition, applications of this theorem to multidimensional projective geometry are indicated and problems illuminating further insight into the theory of Mori extremal rays are formulated. Bibliography: 14 titles.
107 citations
TL;DR: In this article, the author determined when the principally polarized abelian of a Beauville pair satisfying a certain stability type condition is isomorphic to the Jacobian of nonsingular curve.
Abstract: In this paper the author determines when the principally polarized Prymian of a Beauville pair satisfying a certain stability type condition is isomorphic to the Jacobian of a nonsingular curve. As an application, he points out new components in the Andreotti-Mayer variety of principally polarized abelian varieties of dimension whose theta-divisors have singular locus of dimension ; he also proves a rationality criterion for conic bundles over a minimal rational surface in terms of the intermediate Jacobian. The first part of the paper contains the necessary preliminary material introducing the reader to the modern theory of Prym varieties.Figures: 10. Bibliography: 32 titles.
81 citations
Cited by
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TL;DR: In this paper, it was shown that pl-flips exist in dimension n − 1, assuming finite generation in dimension N − 1 and assuming that pl flips exist in all dimensions.
Abstract: Assuming finite generation in dimension n − 1, we prove that pl-flips exist in dimension n.
1,612 citations
TL;DR: In this paper, the revised notes of my lectures at the 1995 Santa Cruz summer institute are presented. Changes from the Jan.26,1996 version: Major: 7.1--2; Medium: 3.7, 3.11, 5.3, 7.9.2, 9.8.
Abstract: These are the revised notes of my lectures at the 1995 Santa Cruz summer institute. Changes from the Jan.26,1996 version: Major: 7.1--2; Medium: 3.7, 3.11, 5.3.3, 7.9.2, 9.8.
573 citations
TL;DR: In this article, the authors introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them, which is based on a reduction to the algebraic case, but takes into account more quantitative informations of great interest for complex analysis and complex differential geometry.
Abstract: We introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar concepts which have been considered e.g. by Arnold and Varchenko, mostly for the study of hypersurface singularities. The plurisubharmonic version is somehow based on a reduction to the algebraic case, but it also takes into account more quantitative informations of great interest for complex analysis and complex differential geometry. We give as an application a new derivation of criteria for the existence of Kahler–Einstein metrics on certain Fano orbifolds, following Nadel's original ideas (but with a drastic simplication in the technique, once the semi-continuity result is taken for granted). In this way, three new examples of rigid Kahler–Einstein Del Pezzo surfaces with quotient singularities are obtained.
408 citations
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TL;DR: In this article, it was shown that 3-fold log flips exist for log canonical and -factorial log terminal models, as well as a positive answer to the inversion problem for logcanonical and log terminal adjunction.
Abstract: We prove that 3-fold log flips exist. We deduce the existence of log canonical and -factorial log terminal models, as well as a positive answer to the inversion problem for log canonical and log terminal adjunction.
301 citations