Some results on linear stability and stability of syzygy bundles |
| Abel Castorena |
| (A joint work with Hugo Torres-López) |
| Centro de Ciencias Matemáticas |
| UNAM-Morelia |
| Abstract: |
| Applying some techniques of Brill-Noether theory for vector bundles over a general curve, we fill-up a proof of a result of Butler about the stability of the syzygy bundle \[M_L\] when \[L\] is a globally generated line bundle over a general curve \[C\] . Following this circle of ideas and when we restrict to \[d\] -gonal curves, we give conditions to obtain the equivalence between the (semi)-stability of \[M_L\] and the linear (semi)-stability of the pair \[(L, H^0(L))\] . This gives a positive answer of a particular case of a conjecture of C. Mistretta and L. Stoppino. |