A smoothness criterion for complex spaces in terms of differential forms - Samuelsson Kalm, Håkan; Sera, Martin (MATHEMATICA SCANDINAVICA, 2020)
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 $ω _X^1$.