Automorphisms of quartic del Pezzo surfaces in characteristic zero

2023/08/15 by Smith, Jonathan M. · 1 citation
#14E08 #14J45 #14J50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2308.07904

Abstract

For each field k of characteristic zero, we classify which groups act by automorphisms on a quartic del Pezzo surface over k. We also determine which groups act on k-rational, stably k-rational, or k-unirational quartic del Pezzo surfaces. For each group G that is realized over k, we exhibit explicit equations for a quartic del Pezzo surface X in ℙ⁴_k such that G acts by automorphisms on X.

Cited by

• Representations of finite subgroups of Cremona groups

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• Quotients of del Pezzo surfaces of high degree
• Automorphisms of del Pezzo surfaces of degree 2 in characteristic 2
• Automorphisms of cubic surfaces in positive characteristic
• Automorphisms of del Pezzo surfaces without points
• Groups acting on cubic surfaces in characteristic zero