Viehweg, Eckart; Zuo, Kang:
Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds
2006
In: Journal of Algebraic Geometry, Jg. 15 (2006), Heft 4, S. 771 - 791
Artikel/Aufsatz in Zeitschrift / Fach: Mathematik
Titel:
Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds
Autor(in):
Viehweg, Eckart; Zuo, Kang
Erscheinungsjahr:
2006
Erschienen in:
Journal of Algebraic Geometry, Jg. 15 (2006), Heft 4, S. 771 - 791
ISSN:
Signatur der UB:
Link URL:

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.