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Semispecial Tensors and Quotients of the Polydisc

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  • Patrick Graf
  • Aryaman Patel

Abstract

Let X$X$ be a complex‐projective variety with klt singularities and ample canonical divisor. We prove that X$X$ is a quotient of the polydisc by a group acting properly discontinuously and freely in codimension one if and only if X$X$ 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.

Suggested Citation

  • Patrick Graf & Aryaman Patel, 2026. "Semispecial Tensors and Quotients of the Polydisc," Mathematische Nachrichten, Wiley Blackwell, vol. 299(5), pages 1045-1061, May.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:5:p:1045-1061
    DOI: 10.1002/mana.70127
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