Double points of plane models in

The aim of this paper is to compute the class of the closure of the effective divisor in M6,1 given by pointed curves [C,p] with a sextic plane model mapping p to a double point. Such a divisor generates an extremal ray in the pseudoeffective cone of as shown by Jensen. A general result on some families of linear series with adjusted Brill–Noether number 0 or −1 is introduced to complete the computation.