Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds
In: Journal of Algebraic Geometry, Vol. 15 (2006), No. 4, pp. 771 - 791
Title:
Numerical bounds for semi-stable families of curves or of certain higher dimensional manifolds
Author:
Viehweg, Eckart;Zuo, Kang
Year of publication:
2006
WWW URL:
Appears in
Title in English (abbreviated):
J. Algebraic Geometry
Title in English (abbreviated):
J Algebraic Geom
Place of publication:
Providence
Publisher:
American Mathematical Society (AMS)
in:
Vol. 15 (2006), No. 4, pp. 771 - 791
ISSN
ISSN
ZDB ID
Library shelfmark:
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.