Extremal effective divisors of Brill-Noether and Gieseker-Petri type in M_1,n
Here, Dawei and I exhibit certain extremal effective divisors on the moduli spaces of marked genus 1 curves which are not of Chen-Coskun type, i.e. they do not arise from imposing group-law linear dependencies on the marked points. The construction begins in M_1,3, where we take a three-pointed elliptic curve, and "crimp" the marked points to create a cuspidal curve of arithmetic genus 4. We then require this curve to be Gieseker-Petri special, i.e. that its canonical model lie in a singular quadric. We show that this construction produces a novel extremal divisor. Might this business of crimping produce more extremal examples in other moduli spaces of marked curves?