Solvability of curves on surfaces

Abstract

In this article, we study subloci of solvable curves in ${\mathcal{M}}_g$ which are contained in either a K3-surface or a quadric or a cubic surface. We give a bound on the dimension of such subloci. In the case of complete intersection genus $g$ curves in a cubic surface, we show that a general such curve is solvable.

11 pages