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.
Numerically flat Higgs vector bundles / Bruzzo, U.; Otero, B. G.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 9:(2007), pp. 437-446. [10.1142/S0219199707002526]
Numerically flat Higgs vector bundles
Bruzzo, U.;
2007-01-01
Abstract
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.| File | Dimensione | Formato | |
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