Double Points of Plane Models in M_{g,1}

The aim of this paper is to compute the class of the closure of the effective divisor in M_{6,1} 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 M_{6,1} 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.