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.