Semispecial tensors and quotients of the polydisc

Abstract

Let $X$ be a complex-projective variety with klt singularities and ample canonical divisor. We prove that $X$ is a quotient of the polydisc by a group acting properly discontinuously and freely in codimension one if and only if $X$ admits a semispecial tensor with reduced hypersurface. This extends a result of Catanese and Di Scala to singular spaces, and answers a question raised by these authors. As a key step in the proof, we establish the Bochner principle for holomorphic tensors on klt spaces in the negative Kähler--Einstein case.

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References in corpus (4)

• Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
• The Miyaoka-Yau inequality and uniformisation of canonical models
• Bogomolov-Sommese vanishing on log canonical pairs
• Kähler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups