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

By D. Greb, Stefan Kebekus, S'andor J. Kov'acs. Compositio Mathematica, 2008

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8875a04b64104891d1f93f715001205cd03db31d

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Singular spaces with trivial canonical class (2011, background): “s across E, to give a p-form on π−1(U). In other words, it asserts that the natural restriction map Ωp Xe π−1(U) → Ωp Xe π−1(U)\ E is surjective. We refer to the original papers [GKKP11, Sect. 1] and [GKK10] or to the survey [Keb11] for an in-depth discussion. 3. IRREGULARITY AND ALBANESE MAP OF CAN”