Arakelov-type inequalities for Hodge bundles

Details Arakelov-type inequalities for Hodge bundles Arakelov-type inequalities for Hodge bundles

2000-07-17

arxiv.org/abs/math/0007102v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

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.

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