A SMOOTHNESS CRITERION FOR COMPLEX SPACES IN TERMS OF DIFFERENTIAL FORMS

Journal article, 2020

For a reduced pure dimensional complex space X, we show that if Barlet's recently introduced sheaf alpha(1)(X) 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(1)(X).