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

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

2005-04-26

arxiv.org/abs/math/0504542v2

Mathematics

Algebraic Geometry

2nd version: LaTeX, 18 pages. The introduction and section 3 were reformulated

Scientific paper

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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