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Numerically flat Higgs vector bundles

TitleNumerically flat Higgs vector bundles
Publication TypePreprint
AuthorsBruzzo, U, Grana-Otero, B
Series TitleCommun. Contemp. Math. 9 (2007) 437-446
Document NumberSISSA;39/2005/FM

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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