Computing the equisingularity type of a pseudo-irreducible polynomial

TL;DR

This paper presents a method to compute the equisingularity type of a specific family of plane curve singularities efficiently, using quasi-linear time algorithms based on discriminant valuation.

Contribution

It introduces a novel quasi-linear time algorithm for determining the equisingularity type of pseudo-irreducible plane curve singularities.

Findings

The algorithm computes the equisingularity type efficiently.

Applicable to a family of singularities including irreducible ones.

Operates in quasi-linear time relative to discriminant valuation.

Abstract

Germs of plane curve singularities can be classified accordingly to their equisingularity type. For singularities over C, this important data coincides with the topological class. In this paper, we characterise a family of singularities, containing irreducible ones, whose equisingularity type can be computed in quasi-linear time with respect to the discriminant valuation of a Weierstrass equation.