# Degenerate abelian function fields

## TL;DR

This paper investigates the properties of abelian function fields associated with singular curves, extending the classical theory from smooth Riemann surfaces to more general algebraic curves.

## Contribution

It introduces a study of abelian function fields in the context of singular curves, expanding the understanding of their structure beyond smooth cases.

## Key findings

- Extended the theory of abelian function fields to singular curves.
- Analyzed the generation of these fields by fundamental abelian functions.
- Provided insights into the relation between meromorphic functions on singular curves and their Jacobians.

## Abstract

Originally, an abelian function field is the field of meromorphic functions on the Jacobi variety J(X) of a compact Riemann surface X. It is generated by the fundamental abelian functions belonging to the meromorphic function field on X. We study this relation for singular curves.