On $pq$-fold regular covers of the projective line

TL;DR

This paper investigates non-abelian pq-fold regular covers of the projective line, providing algebraic models, Jacobian decompositions, and classifications of related Riemann surface families, advancing understanding of these algebraic structures.

Contribution

It introduces a classification of non-abelian pq-fold covers, constructs algebraic models, and offers a general Jacobian isogeny decomposition, extending prior work on Riemann surfaces.

Findings

Algebraic models for special pq-fold covers are determined.

A general isogeny decomposition of Jacobians is provided.

Classification of one-dimensional families of Riemann surfaces is achieved.

Abstract

Let $p$ and $q$ be odd prime numbers. In this paper we study non-abelian pq-fold regular covers of the projective line, determine algebraic models for some special cases and provide a general isogeny decomposition of the corresponding Jacobian varieties. We also give a classification and description of the one-dimensional families of compact Riemann surfaces as before.