Some results on linear stability and stability of syzygy bundles

Abel Castorena
(A joint work with Hugo Torres-López)
Centro de Ciencias Matemáticas
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
is a globally generated line bundle over a general curve
. Following this circle of ideas and when we restrict to
-gonal curves, we give conditions to obtain the equivalence between the (semi)-stability of
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.