Birational classification of pointless del Pezzo surfaces of degree 8

2022/02/22 by Andrey Trepalin, Trepalin, Andrey · 2 citations
Arts and Humanities · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #North African History and Literature

paper · pdf · doi:10.48550/arxiv.2202.11030

openalex publication_date 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a perfect field. Recently J.-L. Colliot-Thélène showed that two pointless quadric surfaces over k are birationally equivalent if and only if they are isomorphic. We show that this result holds for arbitrary del Pezzo surfaces of degree 8 with the Picard number 1, and describe minimal surfaces birationally equivalent to a given pointless del Pezzo surface of degree 8.

Cited by

• Birational geometry of del Pezzo surfaces of degree 4
• The Degree of Irrationality of del Pezzo Surfaces

Related

• Birational geometry of del Pezzo surfaces of degree 4
• Birational Geometry of sextic del Pezzo surfaces
• Unirationality of del Pezzo surfaces of degree two over finite fields (extended version)
• Unirationality of RDP Del Pezzo surfaces of degree 2
• Degree of Unirationality for del Pezzo Surfaces over Finite Fields