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arXiv · 2505.03904

Semispecial tensors and quotients of the polydisc

Patrick Graf·Aryaman Patel
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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 K\"{a}hler--Einstein case.

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Patrick Graf, Aryaman Patel. 2025-05-06. Semispecial tensors and quotients of the polydisc. https://doi.org/10.1002/mana.70127

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