A smoothness criterion for complex spaces in terms of differential forms

Håkan Samuelsson Kalm; Martin Sera

doi:10.7146/math.scand.a-119216

paper

A smoothness criterion for complex spaces in terms of differential forms

arXiv:1709.09833 · doi:10.7146/math.scand.a-119216

Abstract

For a reduced pure dimensional complex space $X$ , we show that if Barlet's recently introduced sheaf $α_{X}^{1}$ 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 $ω_{X}^{1}$ .

8 p; minor corrections