Limits of translates of plane curves -- on a paper of Aldo Ghizzetti

2003/06/24 by Paolo Aluffi, Carel Faber, Aluffi, Paolo +1
Computer Science · Engineering · Mathematics · #14E05 #14H50 #14L35 #14N10 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E05 #msc:14H50 #msc:14L35 #msc:14N10

paper · pdf · doi:10.48550/arxiv.math/0306348

Minor changes. 68 pages, 16 figures

openalex publication_date 2003/06/24 · arxiv created 2003/11/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the limits of PGL(3) translates of an arbitrary plane curve, giving a description of all possible limits of a given curve and computing the multiplicities of corresponding components in the normal cone to the base scheme of a related linear system. This information is a key step in the computation of the degree of the closure of the linear orbit of an arbitrary plane curve. Our analysis recovers and extends results obtained by Aldo Ghizzetti in the 1930's.

Related

• Equivariant Degenerations of Plane Curve Orbits
• Limit linear systems and applications
• Linear Systems of Plane Curves with a Composite Number of Base Points of Equal Multiplicity
• Translation surfaces and their orbit closures: An introduction for a broad audience
• Reduction method for linear systems of plane curves with base fat points