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Abstract <p> We construct an example of a field and a smooth del Pezzo surface of degree <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2\)</EquationSource> </InlineEquation> over this field without points such that its automorphism group is isomorphic to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathrm{PSL}_2(\mathbb{F}_7) \times \mathbb{Z}/2\mathbb{Z}\)</EquationSource> </InlineEquation>, which is the largest possible automorphism group for del Pezzo surfaces of degree <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(2\)</EquationSource> </InlineEquation> over an algebraically closed field of characteristic zero. </p>

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The Largest Automorphism Group of a Del Pezzo Surface of Degree \(2\) without Points

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Anastasia Vikulova

摘要

Abstract

We construct an example of a field and a smooth del Pezzo surface of degree \(2\) over this field without points such that its automorphism group is isomorphic to \(\mathrm{PSL}_2(\mathbb{F}_7) \times \mathbb{Z}/2\mathbb{Z}\) , which is the largest possible automorphism group for del Pezzo surfaces of degree \(2\) over an algebraically closed field of characteristic zero.