Pfaffian representations of plane curves

2018/04/09 by David Oscari, Oscari, David
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1804.02803

openalex publication_date 2018/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a commutative ring with 1. For every homogeneous polynomial f(X₀,X₁,X₂) in R[X₀,X₁,X₂] of degree d <= 25, we find a explicit linear Pfaffian R-representation of f. We describe an empirical method that leads us to find such R-representations. This generalizes and constitutes an alternative proof (up to degree 25) of a result due to A. Beauville [Bea] about the existence of linear Pfaffian K-representations for any smooth plane curve of degree d >= 2, where K is an algebraically closed field of characteristic zero.

Citations

• Determinantal hypersurfaces

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