Arakelov type inequalities for Hodge bundles over algebraic varieties, Part I: Hodge bundles over algebraic curves

Authors:
Jürgen Jost and Kang Zuo

Journal:
J. Algebraic Geom. **11** (2002), 535-546

DOI:
https://doi.org/10.1090/S1056-3911-02-00299-0

Published electronically:
February 13, 2002

MathSciNet review:
1894937

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Abstract | References | Additional Information

Abstract: We prove Arakelov inequalities for systems of Hodge bundles over algebraic varieties, generalizing the classical ones for families of semi-stable curves and abelian varieties. These inequalities are derived from the semi-stability of an associated Higgs bundle, a consequence of the existence of a Hermitian Yang-Mills metric.

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Additional Information

**Jürgen Jost**

Affiliation:
Max Planck Institute for Mathematics, Inselstrasse 22-26, D-04103 Leipzig, Germany

Email:
jost@mis.mpg.de

**Kang Zuo**

Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T. Hong Kong

Email:
kzuo@math.cuhk.edu.hk

DOI:
https://doi.org/10.1090/S1056-3911-02-00299-0

Received by editor(s):
December 2, 1999

Received by editor(s) in revised form:
October 17, 2000

Published electronically:
February 13, 2002

Additional Notes:
The second author was supported by a Heisenberg fellowship of the DFG