Del Pezzo surfaces of degree 5 over perfect fields

2023/04/11 by Aurore Boitrel, Boitrel, Aurore · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2304.05328

openalex publication_date 2023/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the classification of del Pezzo surfaces X of degree 5 over any perfect field k in explicit geometric terms. More precisely, in each case we use the Petersen graph to illustrate the Gal(k/k)-action on the (-1)-curves of X and we describe explicitly its group of automorphisms, Aut_k(X). For the cases when X is not minimal, we describe how to realize it as the blow-up of ℙ², or of a (minimal) quadric in ℙ³, and classify them up to k-isomorphism. In all cases, the elements of the group Aut_k(X) are described geometrically.

Cited by

• A quadratically enriched count of lines on a smooth del Pezzo surface of degree 5
• Representations of finite subgroups of Cremona groups

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