Sharp slope bounds for sweeping families of trigonal curves

Abstract

We establish sharp bounds for the slopes of curves in Mg that sweep out the locus of trigonal curves, reproving Stankova-Frenkel's bound of 7 + 6/g for even g and obtaining the bound 7 + 20/(3g + 1) for odd g. For even g, we find an explicit expression of the so-called Maroni divisor in the Picard group of the space of admissible triple covers. For odd g, we describe the analogous extremal effective divisor and give a similar explicit expression. Show more