Petri Maps for Very Ample Line Bundles

Here we construct several smooth curves C and several very ample and special line bundles L on C such that the multiplication map $H^0(C,L)\otimes H^0(C, \omega_C \otimes L^*) \rightarrow H^0(C, \omega_C)$ (i.e. the Petri map) is surjective.