We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism $s$ of the tensor product $T\otimes T'$ of the tangent bundle $T$ with the cotangent bundle $T'$. To such a curvature type tensor $\s$ one associates the first Mok characteristic cone $CS$, obtained by projecting on $T$ the intersection of $ker (s)$ with the space of rank 1 tensors. The simpler characterization requires that the projective scheme associated to $CS$ be a finite union of projective varieties of given dimensions and codimensions in their linear spans which must be skew and generate.
A characterization of varieties whose universal cover is a bounded symmetric domain without ball factors / DI SCALA, ANTONIO JOSE'; Catanese, F.. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 257:(2014), pp. 567-580. [10.1016/j.aim.2014.02.030]
A characterization of varieties whose universal cover is a bounded symmetric domain without ball factors
DI SCALA, ANTONIO JOSE';
2014
Abstract
We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism $s$ of the tensor product $T\otimes T'$ of the tangent bundle $T$ with the cotangent bundle $T'$. To such a curvature type tensor $\s$ one associates the first Mok characteristic cone $CS$, obtained by projecting on $T$ the intersection of $ker (s)$ with the space of rank 1 tensors. The simpler characterization requires that the projective scheme associated to $CS$ be a finite union of projective varieties of given dimensions and codimensions in their linear spans which must be skew and generate.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2535725
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