IJPAM: Volume 20, No. 4 (2005)

STABLE VECTOR BUNDLES ON REDUCIBLE
CURVES: PRELIMINARY REMARKS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]

Abstract.Here is one of our results. Let be a reduced, but not irreducible projective curve such that all irreducible components of are smooth and rational. Let be a rank vector bundle on . There is at least a polarization on such that is not stable for this polarization. is semistable for all polarizations, if and only if for every irreducible component of . is semistable with respect to a polarization if and only if there is an integer such that .