# Solvability of curves on surfaces

## TL;DR

This paper investigates the conditions under which algebraic curves on surfaces are solvable, providing bounds on the dimensions of such loci and demonstrating that general curves in certain complete intersections are solvable.

## Contribution

It establishes bounds on the dimension of loci of solvable curves on surfaces and proves that general complete intersection curves in cubic surfaces are solvable.

## Key findings

- Bound on the dimension of solvable curve loci in moduli space
- General complete intersection curves in cubic surfaces are solvable
- Identification of surfaces containing solvable curves

## 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.