Semispecial Tensors and Quotients of the Polydisc

Abstract

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