On deformations of singular plane sextics

TL;DR

This paper investigates the deformation classes of complex plane sextic curves with simple singularities, establishing a diffeomorphism criterion for deformation equivalence and outlining enumeration methods, including examples like Zariski pairs.

Contribution

It provides a new criterion linking deformation equivalence to diffeomorphism classes and outlines a method to enumerate all such classes for sextic curves.

Findings

Deformation equivalence corresponds to diffeomorphism of pairs.

A method to enumerate all deformation classes is proposed.

Examples include classical Zariski pairs.

Abstract

We study complex plane projective sextic curves with simple singularities up to equisingular deformations. It is shown that two such curves are deformation equivalent if and only if the corresponding pairs are diffeomorphic. A way to enumerate all deformation classes is outlined, and a few examples are considered, including classical Zariski pairs.