Confocal families of plane algebraic curves

TL;DR

This paper investigates families of plane algebraic curves with shared foci, using a focal map and deformation theory to analyze their properties and relationships.

Contribution

It introduces a reformulation of confocality through a focal map on equiclassical families and studies its fibers with deformation theory.

Findings

Reformulation of confocality via a focal map.

Analysis of fibers using deformation theory.

Enhanced understanding of confocal families' structure.

Abstract

We study families of plane algebraic curves sharing the same set of foci. We reformulate confocality via a focal map on equiclassical families and analyze its fibers using deformation theory.