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Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds

Eckart Viehweg·Kang Zuo
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Abstract

Given an open subset U of a projective curve Y and a smooth family f:V-->U of curves, with semi-stable reduction over Y, we show that for a sub variation of Hodge structures of rank >2 the Arakelov inequality must be strict. For families of n-folds we prove a similar result under the assumption that the (n,0) component of the Higgs bundle defines fibrewise a birational map.

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Eckart Viehweg, Kang Zuo. 2005-06-21. Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds. https://arxiv.org/abs/math/0504542

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