Numerically flat Higgs vector bundles

Research paper by Ugo Bruzzo, Beatriz Graña Otero

Indexed on: 21 Mar '06Published on: 21 Mar '06Published in: Mathematics - Algebraic Geometry


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.