Numerically flat Higgs vector bundles

Details Numerically flat Higgs vector bundles Numerically flat Higgs vector bundles

2006-03-21

arxiv.org/abs/math/0603509v1

Commun. Contemp. Math. 9 (2007), 437-446.

Mathematics

Algebraic Geometry

11 pages

Scientific paper

10.1142/S0219199707002526

After providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.

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