Mathematical Research Letters

Volume 29 (2022)

Number 2

Positivity of the cotangent sheaf of singular Calabi–Yau varieties

Pages: 339 – 372



Cécile Gachet (Laboratoire Mathématiques & Interactions J.A. Dieudonné, Université Côte d’Azur, Nice, France)


We prove that the tangent and the reflexivized cotangent sheaves of any normal projective klt Calabi–Yau or irreducible holomorphic symplectic variety are not pseudoeffective, generalizing results of A. Höring and T. Peternell [21]. We provide examples of Calabi-Yau varieties of small dimension with singularities in codimension 2.

Received 27 November 2020

Accepted 23 February 2021

Published 29 September 2022