Viehweg, Eckart; Zuo, Kang:

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
ISSN: 1056-3911
Zeitschriftenaufsatz / Fach: Mathematik
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 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.