On Spaces Associated with Invariant Divisors on Galois Covers of Riemann Surfaces and Their Applications

Abstract

Let $f:X\to S$ be a Galois cover of Riemann surfaces, with Galois group $G$. In this paper we analyze the $G$-invariant divisors on $X$, and their associated spaces of meromorphic functions, differentials, and $q$-differentials. We generalize the trace formula for non-trivial elements of $G$ on $q$-differentials, as well as the Chevalley--Weil Formula. When $G$ is Abelian or when the genus of $S$ is 0 we prove additional results, and we also determine the non-special $G$-invariant divisors when both conditions are satisfied.

44 pages, exposition improved, added list of notations

References in corpus (3)

• Thomae formula for Abelian covers of ${\mathbb{CP}}^1$
• Thomae Formulae for General Fully Ramified $Z_n$ Curves
• Thomae formula for $2$ Abelian covers of ${\mathbb{CP}}^1$

Cited by in corpus (1)

• Thomae's Derivative Formulae for Trigonal Curves