Resumen de A smoothness criterion for complex spaces in terms of differential forms

Hakan Samuelsson, Martin Sera

• For a reduced pure dimensional complex space X, we show that if Barlet's recently introduced sheaf α1X 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 ω1X.