Publications mathématiques de l'IHÉS

, Volume 114, Issue 1, pp 87–169

Differential forms on log canonical spaces

  • Daniel Greb
  • Stefan Kebekus
  • Sándor J Kovács
  • Thomas Peternell
Article

DOI: 10.1007/s10240-011-0036-0

Cite this article as:
Greb, D., Kebekus, S., Kovács, S.J. et al. Publ.math.IHES (2011) 114: 87. doi:10.1007/s10240-011-0036-0

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.

Copyright information

© IHES and Springer-Verlag 2011

Authors and Affiliations

  • Daniel Greb
    • 1
  • Stefan Kebekus
    • 1
  • Sándor J Kovács
    • 2
  • Thomas Peternell
    • 3
  1. 1.Mathematisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburg im BreisgauGermany
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA
  3. 3.Matematisches InstitutUniversität BayreuthBayreuthGermany