A smoothness criterion for complex spaces in terms of differential forms

Håkan Samuelsson Kalm; Martin Sera

doi:10.7146/math.scand.a-119216

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arXiv · 1709.09833

A smoothness criterion for complex spaces in terms of differential forms

Håkan Samuelsson Kalm·Martin Sera

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Abstract

For a reduced pure dimensional complex space $X$, we show that if Barlet's recently introduced sheaf $\alpha_X^1$ of holomorphic $1$-forms or the sheaf of germs of weakly holomorphic $1$-forms is locally free, then $X$ is smooth. Moreover, we discuss the connection to Barlet's well-known sheaf $\omega_X^1$.

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BibTeX RIS

Håkan Samuelsson Kalm, Martin Sera. 2017-09-28. A smoothness criterion for complex spaces in terms of differential forms. https://doi.org/10.7146/math.scand.a-119216

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