Convex hulls of surfaces in fourspace

2022/09/02 by Chiara Meroni, Kristian Ranestad, Meroni, Chiara +3
Computer Science · Mathematics · #14N05 #14P05 #14P10 #52A99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Metric Geometry (math.MG) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2209.01151

openalex publication_date 2022/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurfaces do. Our method is a detailed analysis of a general purpose formula by Ranestad and Sturmfels in the case of smooth real algebraic surfaces of low degree (that are rational over the complex numbers). We study both the complex and the real features of the algebraic boundary of Veronese, Del Pezzo and Bordiga surfaces.

Related

• On the convex hull of a space curve
• The Convex Hull of a Variety
• The convex hull of a convex space curve with four vertices
• Construction of rational surfaces of degree 12 in projective fourspace (with an appendix by Kristian Ranestad)
• A note on rational surfaces in projective four-space