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arXiv · 1609.02296

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

Yaacov Kopeliovich·Shaul Zemel
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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.

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Yaacov Kopeliovich, Shaul Zemel. 2020-08-11. On Spaces Associated with Invariant Divisors on Galois Covers of Riemann Surfaces and Their Applications. https://doi.org/10.1007/s11856-019-1946-7

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