A smoothness criterion for complex spaces in terms of differential forms

• Håkan Samuelsson Kalm ^[1] ; Martin Sera ^[2]
  1. [1] University of Gothenburg (Suecia)
  2. [2] Kyoto University of Advanced Science (Japón)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 126, Nº 2, 2020, págs. 221-228
• Idioma: inglés
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• Resumen

  • 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.