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 -
TY - JOUR
T1 - Relatively stable bundles over elliptic fibrations
JF - Math. Nachr. 238 (2002) 23-36
Y1 - 2002
A1 - Claudio Bartocci
A1 - Ugo Bruzzo
A1 - Daniel Hernandez Ruiperez
A1 - Jose M. Munoz Porras
AB - 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.
PB - Wiley
UR - http://hdl.handle.net/1963/3132
U1 - 1201
U2 - Mathematics
U3 - Mathematical Physics
ER -