Differential forms on log canonical spaces

By D. Greb, Stefan Kebekus, S'andor J. Kov'acs, T. Peternell. 2010

233 citations recorded by the source corpus.

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting.Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6153a292af6ca4556fb4a4899f7fad7cb927d890

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In Computational Theory and Mathematics

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Citations in the corpus

Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of Abelian varieties (2013, background): “pological fundamental group π1(Yan). A locally free, algebraic sheaf on Y is called ﬂat if and only if the associated analytic sheaf is ﬂat. UsingthepartialsolutionoftheLipman-Zariskiconjectureshownin[GKKP11], we obtain the following criterion for a klt space to have quotient singularities. We alsoo”