A note on Flenner's extension theorem

Abstract

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