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

Jürgen Jost and Kang Zuo

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Submission date: 29. Feb. 2000
Pages: 15
published in: Journal of algebraic geometry, 11 (2002) 3, p. 535-546 
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Abstract:
We prove Arakelov inequalities for systems of Hodge bundles over algebraic varieties, generalizing the classical ones for families of semistable curves and abelian varieties. These inequalities are derived from the semistability of an associated Higgs bundle, a consequence of the existence of a Hermitian Yang-Mills metric.