International Journal of Mathematics ( IF 0.604 ) Pub Date : 2020-06-23 , DOI: 10.1142/s0129167x20500548 Sonia Brivio; Filippo F. Favale
Given a vector bundle on a complex reduced curve and a subspace of which generates , one can consider the kernel of the evaluation map , i.e. the kernel bundle associated to the pair . Motivated by a well-known conjecture of Butler about the semistability of and by the results obtained by several authors when the ambient space is a smooth curve, we investigate the case of a reducible curve with one node. Unexpectedly, we are able to prove results which goes in the opposite direction with respect to what is known in the smooth case. For example, is actually quite never -semistable. Conditions which gives the -semistability of when or when is a line bundle are then given.