ORBIFOLD CHERN CLASSES INEQUALITIES AND APPLICATIONS
| Autor: | Erwan Rousseau, Behrouz Taji |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Mathematisches Institut [Freiburg], Albert-Ludwigs-Universität Freiburg, University of Notre Dame [Indiana] (UND), ANR-16-CE40-0008,Foliage,Feuilletages et géométrie algébrique(2016) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: | |
| Popis: | In this paper we prove that given a pair $(X,D)$ of a threefold $X$ and a boundary divisor $D$ with mild singularities, if $(K_X+D)$ is movable, then the orbifold second Chern class $c_2$ of $(X,D)$ is pseudo-effective. This generalizes the classical result of Miyaoka on the pseudo-effectivity of $c_2$ for minimal models. As an application we give a simple solution to Kawamata's effective non-vanishing conjecture in dimension $3$, where we prove that $H^0(X, K_X+H)\neq 0$, whenever $K_X+H$ is nef and $H$ is an ample, effective, reduced Cartier divisor. Furthermore, we study Lang-Vojta's conjecture for codimension one subvarieties and prove that minimal varieties of general type have only finitely many Fano, Calabi-Yau or Abelian subvarieties of codimension one, mildly singular, whose classes belong to the movable cone. Comment: 22 pages. Corrections in Sections 3 and 6. Main results unchanged |
| Databáze: | OpenAIRE |
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