Minimal degree equations for curves and surfaces (variations on a theme\n of Halphen)

2019/06/19 by Edoardo Ballico, Ballico, Edoardo, Emanuele Ventura +1
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1906.08117

openalex publication_date 2019/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many classical results in algebraic geometry arise from investigating some\nextremal behaviors that appear among projective varieties not lying on any\nhypersurface of fixed degree. We study two numerical invariants attached to\nsuch collections of varieties: their minimal degree and their maximal number of\nlinearly independent smallest degree hypersurfaces passing through them. We\nshow results for curves and surfaces, and pose several questions.\n

Related

• Rational curves of minimal degree and characterizations of \mathbb Pⁿ
• On the minimal degree of morphisms between algebraic curves
• Minimal degree fibrations in curves and the asymptotic degree of irrationality of divisors
• Subspace configurations and low degree points on curves
• A note on special polynomials and minimal surfaces