Pullback 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 "pullback form" on X. The pullback map obtained by this construction is O_Ylinear, 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 arXiv:
 arXiv:1210.3255
 Bibcode:
 2012arXiv1210.3255K
 Keywords:

 Mathematics  Algebraic Geometry;
 14J17;
 14B05
 EPrint:
 Final version, to appear in Advances in Mathematics