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arXiv · 1210.3255

Pull-back Morphisms for Reflexive Differential Forms

Stefan Kebekus
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Abstract

Let f : X -> Y be a morphism between normal complex varieties, and assume that Y is Kawamata log terminal. Given any differential form, defined on the smooth locus of Y, we construct a "pull-back form" on X. The pull-back map obtained by this construction is O_Y-linear, uniquely determined by natural universal properties and exists even in cases where the image of f is entirely contained in the singular locus of the target variety Y. One relevant setting covered by the construction is that where f is the inclusion (or normalisation) of the singular locus of Y. As an immediate corollary, we show that differential forms defined on the smooth locus of Y induce forms on every stratum of the singularity stratification. The same result also holds for many Whitney stratifications.

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Stefan Kebekus. 2013-06-12. Pull-back Morphisms for Reflexive Differential Forms. https://doi.org/10.1016/j.aim.2013.06.013

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