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arXiv · 1811.03644

Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities

Stefan Kebekus·Christian Schnell
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Abstract

We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient condition for this, whose proof relies on the Decomposition Theorem and Saito's theory of mixed Hodge modules. We use it to generalize the theorem of Greb-Kebekus-Kovács-Peternell to complex spaces with rational singularities, and to prove the existence of a functorial pull-back for reflexive differentials on such spaces. We also use our methods to settle the "local vanishing conjecture" proposed by Mustaţă, Olano, and Popa.

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Stefan Kebekus, Christian Schnell. 2020-07-13. Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities. https://doi.org/10.1090/jams%2F962

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