## 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.