Irreducibility of the equiclassical locus
Let D be a reduced plane curve and p a singular point of D. We know there exists an étale miniversal deformation space for the pair (D,p). Inside the base of this deformation space there are various loci that parametrize deformations of (D,p) that preserve certain properties of the singularity. We will be concerned with the equiclassical locus EC which parametrizes deformations of (D,p) in which the singularity is allowed to possibly break up into several singularities but it is required that the total local contribution of all these singularities to the geometric genus of a plane curve and to the class of a plane curve (that is the degree of its dual) must both remain constant. We determine for which singularities, (D,p), EC is singular and show that when EC is singular it has a unibranched singularity with a nonsingular normalization.
scientific article; zbMATH DE number 4051770