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
DOI:
https://doi.org/10.1090/S1056-3911-05-00423-6
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
Email:
viehweg@uni-essen.de
Kang Zuo
Affiliation:
Universität Mainz, Fachbereich 17, Mathematik, 55099 Mainz, Germany
MR Author ID:
269893
Email:
kzuo@mathematik.uni-mainz.de
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
