Extension theorems for differential forms and Bogomolov-Sommese vanishing on log canonical varieties

摘要

Given a p-form defined on the smooth locus of a normal variety, and aresolution of singularities, we study the problem of extending the pull-back ofthe p-form over the exceptional set of the desingularization. For log canonical pairs and for certain values of p, we show that anextension always exists, possibly with logarithmic poles along the exceptionalset. As a corollary, it is shown that sheaves of reflexive differentials enjoygood pull-back properties. A natural generalization of the well-knownBogomolov-Sommese vanishing theorem to log canonical threefold pairs follows.