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A smoothness criterion for complex spaces in terms of differential forms. (arXiv:1709.09833v1 [math.CV])

来源于:arXiv
On a reduced complex space $X$, weakly holomorphic $1$-forms are holomorphic $1$-forms on the regular part $X_{\mathrm{reg}}$ that extend holomorphically across the exceptional set of a resolution of singularities of $X$. We show that if the sheaf of germs of weakly holomorphic $1$-forms on $X$ is locally free, then $X$ is smooth. 查看全文>>