Semistability vs. nefness for (Higgs) vector bundles
| dc.creator | Bruzzo, U. | |
| dc.creator | Ruiperez, D. Hernandez | |
| dc.date | 2003-10-03 | |
| dc.date | 2005-04-20 | |
| dc.date.accessioned | 2026-07-07T06:30:38Z | |
| dc.date.available | 2026-07-07T06:30:38Z | |
| dc.description | According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E. | |
| dc.description | Comments: 20 pages, Latex2e, no figures. v2 includes a generalization to complex projective manifolds of any dimension. To appear in Diff. Geom. Appl | |
| dc.identifier | https://arxiv.org/abs/math/0310040 | |
| dc.identifier | http://arxiv.org/abs/math/0310040 | |
| dc.identifier | Diff. Geom. Appl. 24 (2006) 403-416 | |
| dc.identifier | doi:10.1016/j.difgeo.2005.12.007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98389 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20; 14F05; 14H60 | |
| dc.title | Semistability vs. nefness for (Higgs) vector bundles | |
| dc.type | text |