%0 Generic %1 kebekus2018extending %A Kebekus, Stefan %A Schnell, Christian %D 2018 %K Extension %T Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities %U http://arxiv.org/abs/1811.03644 %X We investigate under what conditions holomorphic forms defined on the regular locus of a complex space will extend to a resolution of singularities. Our main result, proved using Hodge modules and the Decomposition Theorem, is that on any reduced complex space of constant dimension $n$, the extension problem for all holomorphic forms is controlled by what happens for holomorphic $n$-forms. This implies the existence of a functorial pull-back for reflexive differentials on spaces with rational singularities. We also prove a variant of the main result for forms with logarithmic poles, and use our methods to settle the "local vanishing conjecture" proposed by Mustata, Olano, and Popa.

@misc{kebekus2018extending, abstract = {We investigate under what conditions holomorphic forms defined on the regular locus of a complex space will extend to a resolution of singularities. Our main result, proved using Hodge modules and the Decomposition Theorem, is that on any reduced complex space of constant dimension $n$, the extension problem for all holomorphic forms is controlled by what happens for holomorphic $n$-forms. This implies the existence of a functorial pull-back for reflexive differentials on spaces with rational singularities. We also prove a variant of the main result for forms with logarithmic poles, and use our methods to settle the "local vanishing conjecture" proposed by Musta\c{t}\u{a}, Olano, and Popa.}, added-at = {2018-11-13T01:50:43.000+0100}, author = {Kebekus, Stefan and Schnell, Christian}, biburl = {https://www.bibsonomy.org/bibtex/2a71b6dc24704124f000685fac0a3acb5/taka3617}, description = {Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities}, interhash = {86dc84084c334ef45718692ae2d10b9a}, intrahash = {a71b6dc24704124f000685fac0a3acb5}, keywords = {Extension}, note = {cite arxiv:1811.03644Comment: Any comments or questions are welcome!}, timestamp = {2018-11-13T01:50:43.000+0100}, title = {Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities}, url = {http://arxiv.org/abs/1811.03644}, year = 2018 }