Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



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

Authors: Eckart Viehweg and Kang Zuo
Journal: J. Algebraic Geom. 15 (2006), 771-791
Published electronically: November 30, 2005
MathSciNet review: 2237270
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Abstract | References | Additional Information

Abstract: Given an open subset $U$ of a projective curve $Y$ and a smooth family $f:V\to U$ of curves, with semi-stable reduction over $Y$, we show that for a subvariation $\mathbb {V}$ of Hodge structures of $R^1f_*\mathbb {C}_V$ with $\textrm {rank} (\mathbb {V})>2$ 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 $\mathbb {V}$ defines a birational map.

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Additional Information

Eckart Viehweg
Affiliation: Universität Duisburg-Essen, Mathematik, 45117 Essen, Germany

Kang Zuo
Affiliation: Universität Mainz, Fachbereich 17, Mathematik, 55099 Mainz, Germany
MR Author ID: 269893

Received by editor(s): April 26, 2005
Received by editor(s) in revised form: June 21, 2005
Published electronically: November 30, 2005
Additional Notes: This work has been supported by the “DFG-Schwerpunktprogramm Globale Methoden in der Komplexen Geometrie”, and by the DFG-Leibniz program