English

A note on Flenner's extension theorem

Algebraic Geometry 2022-01-19 v1 Commutative Algebra Complex Variables

Abstract

We show that any pp-form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as long as pcodimX(Xsg)2p \le \mathrm{codim}_X (X_{\mathrm{sg}}) - 2, where cc 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.

Keywords

Cite

@article{arxiv.1905.01983,
  title  = {A note on Flenner's extension theorem},
  author = {Patrick Graf},
  journal= {arXiv preprint arXiv:1905.01983},
  year   = {2022}
}
R2 v1 2026-06-23T08:58:01.955Z