Computing the space of differential forms of a plane curve and its Cartier-Manin matrix

2022/03/22 by Momonari Kudo, Kudo, Momonari, Shushi Harashita +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2203.11801

openalex publication_date 2022/03/22 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a feasible algorithm to give an explicit basis of the space of regular differential forms on the nonsingular projective model of any given plane algebraic curve. The algorithm is demonstrated for concrete examples, with our implementation over the computer algebra system Magma. As an application, we also describe the Cartier-Manin matrix of the nonsingular projective curve with respect to the basis computed by the algorithm.

Related

• The differential equation satisfied by a plane curve of degree n
• Curve equations from expansions of 1-forms at a nonrational point
• Order one differential equations on nonisotrivial algebraic curves
• Projective structures and Hodge theory
• Differential forms on the curves associated to Appell-Lauricella hypergeometric series and the Cartier operator on them