@article {2006,
title = {Semistability vs. nefness for (Higgs) vector bundles},
journal = {Differential Geom. Appl. 24 (2006) 403-416},
number = {arXiv.org;math/0310040v3},
year = {2006},
abstract = {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.},
doi = {10.1016/j.difgeo.2005.12.007},
url = {http://hdl.handle.net/1963/2237},
author = {Ugo Bruzzo and Daniel Hernandez Ruiperez}
}
@article {2002,
title = {Relatively stable bundles over elliptic fibrations},
journal = {Math. Nachr. 238 (2002) 23-36},
number = {arXiv.org;math/0109123v2},
year = {2002},
publisher = {Wiley},
abstract = {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.},
url = {http://hdl.handle.net/1963/3132},
author = {Claudio Bartocci and Ugo Bruzzo and Daniel Hernandez Ruiperez and Jose M. Munoz Porras}
}