Double total ramifications for curves of genus 2
arXiv:1401.3057
Abstract
Inside the moduli space of curves of genus 2 with 2 marked points we consider the loci of curves admitting a map to P^1 of degree d totally ramified over the two marked points, for d>= 2. Such loci have codimension two. We compute the class of their compactifications in the moduli space of stable curves. Several results will be deduced from this computation.
Final version to appear in International Mathematics Research Notices