An algorithm for computing differential equations for invariant curves

2017/08/28 by Malagón, Camilo Sanabria
Computer Science · Engineering · Mathematics · #14H37 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1708.08555

openalex publication_date 2017/08/28 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28

Abstract

In this paper we describe an algorithm based on the Picard-Vessiot theory that constructs, given any curve invariant under a finite linear algebraic group over the complex numbers, an ordinary linear differential equation whose Schwarz map parametrizes it.

Related

• Schwarz maps of Algebraic Linear Ordinary Differential Equations
• A note on the inverse problem for finite differential Galois groups
• Differential equations defined on algebraic curves
• The differential equation satisfied by a plane curve of degree n
• Linear differential operators for generic algebraic curves