%0 Journal Article
%J Differential Geom. Appl. 24 (2006) 403-416
%D 2006
%T Semistability vs. nefness for (Higgs) vector bundles
%A Ugo Bruzzo
%A Daniel Hernandez Ruiperez
%X 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.
%B Differential Geom. Appl. 24 (2006) 403-416
%G en_US
%U http://hdl.handle.net/1963/2237
%1 2007
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-16T09:06:35Z\\nNo. of bitstreams: 1\\n0310040v3.pdf: 216788 bytes, checksum: 574f5aac93686c2348a6313bd129cb61 (MD5)
%R 10.1016/j.difgeo.2005.12.007
%0 Journal Article
%J Math. Nachr. 238 (2002) 23-36
%D 2002
%T Relatively stable bundles over elliptic fibrations
%A Claudio Bartocci
%A Ugo Bruzzo
%A Daniel Hernandez Ruiperez
%A Jose M. Munoz Porras
%X We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah\\\'s and Tu\\\'s results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.
%B Math. Nachr. 238 (2002) 23-36
%I Wiley
%G en_US
%U http://hdl.handle.net/1963/3132
%1 1201
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-17T07:37:19Z\\nNo. of bitstreams: 1\\n0109123v2.pdf: 199719 bytes, checksum: b8757f4871a0f0fd621bc8f115792a5c (MD5)