The Alexander module of a trigonal curve. II

TL;DR

This paper completes the classification of potential roots of the Alexander polynomial for trigonal curves, considering both conventional and finite field cases, without assuming properness or irreducibility.

Contribution

It provides a comprehensive enumeration of Alexander polynomial roots for trigonal curves, extending previous work to include non-proper and reducible cases.

Findings

Complete list of roots of Alexander polynomial for trigonal curves.

Includes roots over finite fields and complex numbers.

Applies to both proper and reducible curves.

Abstract

We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.