Irreducibility of the equiclassical locus
type: Item
instance of: scholarly article
title: Irreducibility of the equiclassical locus
zbMATH Open document ID: 0645.14001
published in: Journal of Differential Geometry
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14B07
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 4051770
zbMATH Keywords: deformation of singularity
zbMATH Keywords: equiclassical locus
zbMATH Keywords: EC
zbMATH Keywords: plane curve
Wikidata QID: Q115182707
author: Steven P. Diaz
reviewed by: Sonia Pérez Díaz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214443060
OpenAlex ID: W1580361016
DOI: 10.4310/JDG/1214443060
description: scientific article; zbMATH DE number 4051770