Abstract
Let X be a complex hyperbolic space form of finite volume, and W ⊂ X be a complex-analytic subvariety. Let S ⊂ X be a locally closed complex submanifold lying on W which is totally geodesic with respect to the canonical Kähler-Einstein metric on X. We prove that the Zariski closure of S in W is a totally geodesic subset. The latter implies that the Gauss map on any complex-analytic subvariety W ⊂ X is generically finite unless W is totally geodesic.
Partially supported by CERG 7034/04P of the Research Grants Council, Hong Kong.
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Dedicated to Linda Rothschild on the occasion of her 60th birthday
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Mok, N. (2010). On the Zariski Closure of a Germ of Totally Geodesic Complex Submanifold on a Subvariety of a Complex Hyperbolic Space Form of Finite Volume. In: Complex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0009-5_17
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DOI: https://doi.org/10.1007/978-3-0346-0009-5_17
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