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
Full-text PDF

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 $ {\rm 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.

References [Enhancements On Off] (What's this?)

Additional Information

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

Kang Zuo
Affiliation: Universität Mainz, Fachbereich 17, Mathematik, 55099 Mainz, Germany

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

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
AMS Website