A smoothness criterion for complex spaces in terms of differential forms

  • Håkan Samuelsson Kalm
  • Martin Sera

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 $\omega _X^1$.

References

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Published
2020-05-06
How to Cite
Samuelsson Kalm, H., & Sera, M. (2020). A smoothness criterion for complex spaces in terms of differential forms. MATHEMATICA SCANDINAVICA, 126(2), 221-228. https://doi.org/10.7146/math.scand.a-119216
Section
Articles