Tadashi Ashikaga (Tohoku Gakuin University)

Space of moduli maps and Castelnuovo-Horikawa index

Abstract

Castelnuovo-Horikawa index is the invariant of fiber germ of genus 3 which expresses the geographical distance from the Castelnuovo line c_1^2=3p_g-7. We calculate it mainly by pulling back a certain invariant on the moduli space of curves via the moduli map. We also comment on the joint work with Y. Matsumoto about the universal degenerating family of curves using the space of moduli maps.