Confocal families of plane algebraic curves

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.

We added an appendix written by E.Shustin (Tel Aviv University) in which he settles our main conjecture 3.9 in a number of cases not covered by the previous version