Unirationality of cubic hypersurfaces

2000/05/15 by Janós Kollár, János Kollár, Kollár, János · 4 citations
Mathematics · #14G05 14G15 (Primary) 11G25 11D25 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #msc:11D25 #msc:11G25 #msc:14G05 #msc:14G15

paper · pdf · doi:10.48550/arxiv.math/0005146

11 pages, LaTeX

arxiv created 2000/05/15 · openalex publication_date 2000/05/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Segre proved that a smooth cubic surface over Q is unirational iff it has a rational point. We prove that the result also holds for cubic hypersurfaces over any field, including finite fields.

Cited by

• Anomaly cancellation for a U(1) factor
• Low degree subvarieties of universal hypersurfaces
• Equivariant geometry of cubic threefolds with non-isolated singularities
• Smooth Fano 3-folds satisfying Condition (A)

Related

• Unirationality and geometric unirationality for hypersurfaces in positive characteristics
• How often does a cubic hypersurface have a rational point?
• On forms of the Segre cubic
• Rational points on cubic hypersurfaces over \mathbbF_q(t)
• Cubic surfaces with one rational line over finite fields