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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.
Greb, Daniel 1 ; Kebekus, Stefan 1 ; Kovács, Sándor J 2 ; Peternell, Thomas 3
@article{PMIHES_2011__114__87_0,
author = {Greb, Daniel and Kebekus, Stefan and Kov\'acs, S\'andor J and Peternell, Thomas},
title = {Differential forms on log canonical spaces},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {87--169},
publisher = {Springer-Verlag},
volume = {114},
year = {2011},
doi = {10.1007/s10240-011-0036-0},
zbl = {1258.14021},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0036-0/}
}
TY - JOUR AU - Greb, Daniel AU - Kebekus, Stefan AU - Kovács, Sándor J AU - Peternell, Thomas TI - Differential forms on log canonical spaces JO - Publications Mathématiques de l'IHÉS PY - 2011 SP - 87 EP - 169 VL - 114 PB - Springer-Verlag UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0036-0/ DO - 10.1007/s10240-011-0036-0 LA - en ID - PMIHES_2011__114__87_0 ER -
%0 Journal Article %A Greb, Daniel %A Kebekus, Stefan %A Kovács, Sándor J %A Peternell, Thomas %T Differential forms on log canonical spaces %J Publications Mathématiques de l'IHÉS %D 2011 %P 87-169 %V 114 %I Springer-Verlag %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-011-0036-0/ %R 10.1007/s10240-011-0036-0 %G en %F PMIHES_2011__114__87_0
Greb, Daniel; Kebekus, Stefan; Kovács, Sándor J; Peternell, Thomas. Differential forms on log canonical spaces. Publications Mathématiques de l'IHÉS, Tome 114 (2011), pp. 87-169. doi: 10.1007/s10240-011-0036-0
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