Differential forms on log canonical spaces

Daniel Greb; Stefan Kebekus; Sándor J Kovács; Thomas Peternell

doi:10.1007/s10240-011-0036-0

Daniel Greb ¹; Stefan Kebekus ¹ ; Sándor J Kovács ² ; Thomas Peternell ³

¹ Mathematisches Institut, Albert-Ludwigs-Universität Freiburg Eckerstraße 1, 79104, Freiburg im Breisgau Germany
² Department of Mathematics, University of Washington Box 354350, Seattle, WA, 98195 USA
³ Matematisches Institut, Universität Bayreuth 95440, Bayreuth Germany

Publications Mathématiques de l'IHÉS, Volume 114 (2011), pp. 87-169

Abstract

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.

Received: 2010-05-20
Accepted: 2011-06-01
Online First: 2011-10-06
Published online: 2011-11-07

Zbl

DOI: 10.1007/s10240-011-0036-0

Author's affiliations:

Daniel Greb ¹; Stefan Kebekus ¹; Sándor J Kovács ²; Thomas Peternell ³

¹ Mathematisches Institut, Albert-Ludwigs-Universität Freiburg Eckerstraße 1, 79104, Freiburg im Breisgau Germany
² Department of Mathematics, University of Washington Box 354350, Seattle, WA, 98195 USA
³ Matematisches Institut, Universität Bayreuth 95440, Bayreuth Germany

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Daniel Greb; Stefan Kebekus; Sándor J Kovács; Thomas Peternell. Differential forms on log canonical spaces. Publications Mathématiques de l'IHÉS, Volume 114 (2011), pp. 87-169. doi: 10.1007/s10240-011-0036-0

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