Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds
In: Journal of Algebraic Geometry, Jg. 15 (2006) ; Nr. 4, S. 771 - 791
Zeitschriftenaufsatz / Fach: Mathematik
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 subvariation V of Hodge structures of R1f∗CV with rank(V) > 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 of V defines a birational map.