AbstractGiven a normal variety Z, a p-form σ defined on the smooth locus of Z and a resolution of singularities , we study the problem of extending the pull-back π*(σ) over the π-exceptional set . 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.
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