Mathematical Research Letters

Volume 18 (2011)

Number 6

Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities

Pages: 1259 – 1269



Daniel Greb (Institut für Mathematik, Albert–Ludwigs–Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany)

Sönke Rollenske (Sönke Rollenske, Fakultät für Mathematik, Universtät Bielefeld, Universitäts str. 25, 33615 Bielefeld, Germany)


We give a criterion for the sheaf of Kähler differentials on a cone over a smooth projective variety to be torsion-free. Applying this to Veronese embeddings of projective space and using known results about differentials on quotient singularities we show that even for mild, e.g. Gorenstein terminal, singularities the sheaf of Kähler differentials will in general have torsion and cotorsion.

Published 20 February 2012