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

@article{Kebekus2018ExtendingHF,
  title={Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities},
  author={Stefan Kebekus and C. Schnell},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
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-Kov\'acs-Peternell to complex spaces with rational singularities, and to prove the existence of a… Expand

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