A note on Flenner's extension theorem
Algebraic Geometry
2022-01-19 v1 Commutative Algebra
Complex Variables
Abstract
We show that any -form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as long as , where is the codimension of the singular locus. A stronger version of this result, allowing no poles at all, is originally due to Flenner. Our proof, however, is not only completely different, but also shorter and technically simpler. We furthermore give examples to show that the statement fails in positive characteristic.
Cite
@article{arxiv.1905.01983,
title = {A note on Flenner's extension theorem},
author = {Patrick Graf},
journal= {arXiv preprint arXiv:1905.01983},
year = {2022}
}