Title: 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.