Some results on linear stability for syzygy bundles over curves.
Abel Castorena (UNAM Morelia)
Aula Beltrami – Mercoledì 11 Dicembre 2019 h.16:00
Abstract. We consider over a curve C a complete and generated linear series (L, H^0(L)) of type (d,r+1). Denote by M_L the kernel of the evaluation map induced by L. We call the vector bundle M_L a syzygy bundle.
We use classic techniques of Brill-Noether theory to give conditions to determinate the stability of M_L over a general curve in the sense of Brill-Noether. These conditions were first stated by Butler but we believe that there is a gap in their proof.
In this circle of ideas, we consider general curves to give a positive answer to a conjecture of E. Mistretta and L. Stoppino with respect to the equivalence between linear (semi)stability of (L, H^0(L)) and (semi)stability for M_L.
Moreover we show that this conjecture is true in the hyperelliptic case. We believe that this conjecture is not true for every curve, for that , I will discuss some ideas about it.