TY - JOUR
T1 - Semistability vs. nefness for (Higgs) vector bundles
JF - Differential Geom. Appl. 24 (2006) 403-416
Y1 - 2006
A1 - Ugo Bruzzo
A1 - Daniel Hernandez Ruiperez
AB - 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.
UR - http://hdl.handle.net/1963/2237
U1 - 2007
U2 - Mathematics
U3 - Mathematical Physics
ER -