Results 1 to 10 of about 818 (55)
On log canonical divisors that are log quasi-numerically positive
Open Mathematics, 2004 Let $(X, \Delta)$ be a four-dimensional log variety that is projective over the field of complex numbers. Assume that $(X, \Delta)$ is not Kawamata log terminal (klt) but divisorial log terminal (dlt).
Fukuda Shigetaka
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On the connectedness principle and dual complexes for generalized pairs
Forum of Mathematics, Sigma, 2023 Let $(X,B)$ be a pair, and let $f \colon X \rightarrow S$ be a contraction with $-({K_{X}} + B)$ nef over S. A conjecture, known as the Shokurov–Kollár connectedness principle, predicts that $f^{-1} (s) \cap \operatorname ...
Stefano Filipazzi, Roberto Svaldi
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Divisorial contractions to codimension three orbits [PDF]
Épijournal de Géométrie Algébrique, 2021 Let $G$ be a connected algebraic group. We study $G$-equivariant extremal contractions whose centre is a codimension three $G$-simply connected orbit. In the spirit of an important result by Kawakita in 2001, we prove that those contractions are weighted
Samuel Boissière, Enrica Floris
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Fano-type surfaces with large cyclic automorphisms
Forum of Mathematics, Sigma, 2021 We give a characterisation of Fano-type surfaces with large cyclic automorphisms. As an application, we give a characterisation of Kawamata log terminal $3$ -fold singularities with large class groups of rank at least $2$ .
Joaquín Moraga
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The Mori fan of the Dolgachev-Nikulin-Voisin family in genus $2$ [PDF]
Épijournal de Géométrie Algébrique, 2022 In this paper we study the Mori fan of the Dolgachev-Nikulin-Voisin family in degree $2$ as well as the associated secondary fan. The main result is an enumeration of all maximal dimensional cones of the two fans.
Klaus Hulek, Carsten Liese
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Crepant semi-divisorial log terminal model [PDF]
Épijournal de Géométrie Algébrique, 2021 We prove the existence of a crepant sdlt model for slc pairs whose irreducible components are normal in codimension one.
Kenta Hashizume
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Remark on complements on surfaces
Forum of Mathematics, Sigma, 2023 We give an explicit characterization on the singularities of exceptional pairs in any dimension. In particular, we show that any exceptional Fano surface is $\frac {1}{42}$ -lc.
Jihao Liu
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The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class
Forum of Mathematics, Sigma, 2021 Let X be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that X admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth.
Patrick Graf, Martin Schwald
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On the minimal model program for projective varieties with pseudo-effective tangent sheaf [PDF]
Épijournal de Géométrie Algébrique, 2023 In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be decomposed into Fano ...
Shin-ichi Matsumura
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Nonsolidity of uniruled varieties
Forum of Mathematics, Sigma, 2023 We give conditions for a uniruled variety of dimension at least 2 to be nonsolid. This study provides further evidence to a conjecture by Abban and Okada on the solidity of Fano 3-folds.
Livia Campo, Tiago Duarte Guerreiro
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