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.

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关于 Flenner 扩展定理的注释

我们表明，只要 $p \le \mathrm{codim}_X (X_{\mathrm{sg }}) - 2$，其中 $c$ 是奇异位点的余维。这个结果的一个更强的版本，根本不允许极点，最初是由于弗伦纳。然而，我们的证明不仅完全不同，而且更短，技术上更简单。我们进一步举例说明该陈述在积极特征上是失败的。