Abstract
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. Horing and T. Peternell arXiv:1710.06183v2 [math.AG]. We provide examples of Calabi-Yau varieties of small dimension with singularities in codimension 2.
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