Arakelov-type inequalities for Hodge bundles

Abstract

We give a proof of generalizations of the classical Arakelov inequality valid for the degree $d$ of the relative canoincal bundle of a family of curves of genus $g$ over a complete curve of genus $p$ under the assumption that the monodromy around the singular fibers is unipotent. This relative canonical bundle is the (canonical extension of) the Hodge bundle and the inequality is generalized to the degrees of the Hodge bundles of a complex variation of Hodge structures.

11 pages

Cited by in corpus (11)

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• Heights of mixed motives
• Families of abelian varieties over curves with maximal Higgs field
• Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
• On manifolds with holomorphic normal projective connections
• Arakelov (in)equalities
• Remarks on BCOV invariants and degenerations of Calabi-Yau manifolds