An algorithm for computing the Arf closure of an algebroid curve with more than one branch

TL;DR

This paper introduces a fast algorithm to compute the Arf closure of multi-branch algebroid curves, extending previous methods that were limited to single-branch cases, thereby broadening computational capabilities in algebraic geometry.

Contribution

It generalizes an existing algorithm to handle algebroid curves with multiple branches, improving efficiency and applicability.

Findings

Developed a faster algorithm for multi-branch cases

Extended the applicability of Arf closure computations

Validated the algorithm's effectiveness on complex curves

Abstract

In this paper, we give a fast algorithm for the computation of the Arf closure of an algebroid curve with more than one branch, generalizing an algorithm presented by Arslan and Sahin for the algebroid branch case.