Application of classical invariant theory to biholomorphic classification of plane curve singularities, and associated binary forms

2011/06/13 by Alexander Isaev, Isaev, Alexander
Computer Science · Mathematics · #14H20 #14L24 #32S05 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CV #msc:14H20 #msc:14L24 #msc:32S05

paper · pdf · doi:10.48550/arxiv.1106.2602

openalex publication_date 2011/06/13 · arxiv created 2011/10/13 · arxiv updated 2011/10/17 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We use classical invariant theory to solve the biholomorphic equivalence problem for two families of plane curve singularities previously considered in the literature. Our calculations motivate an intriguing conjecture that proposes a way of extracting a complete set of invariants of homogeneous plane curve singularities from their moduli algebras.

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