Extension theorems for differential forms and Bogomolov–Sommese vanishing on log canonical varieties
Daniel Greb, Stefan Kebekus, Sándor J. Kovács · Compositio Mathematica · 2009
Abstract Given a normal variety Z , a p -form σ defined on the smooth locus of Z and a resolution of singularities $\pi : \widetilde {Z} \to Z$ , we study the problem of extending the pull-back π * ( σ ) over the π -exceptional set $E \subset \widetilde {Z}$ . For log canonical pairs and for certain values of p , we show that an extension always exists, possibly with logarithmic poles along E . As a corollary, it is shown that sheaves of reflexive differentials enjoy good pull-back properties. A natural generalization of the well-known Bogomolov–Sommese vanishing theorem to log canonical threefold pairs follows.