Pull-back Morphisms for Reflexive Differential Forms

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.

Final version, to appear in Advances in Mathematics

References in corpus (4)

• Differential Forms on Log Canonical Spaces
• The structure of surfaces mapping to the moduli stack of canonically polarized varieties
• Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks
• Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities

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• Failure of the Brauer-Manin principle for a simply connected fourfold over a global function field, via orbifold Mordell
• Bogomolov's inequality and Higgs sheaves on normal varieties in positive characteristic
• Low degree Hodge theory for klt varieties
• Uniformisation of higher-dimensional minimal varieties
• The symplectic form associated to a singular Poisson algebra
• A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four