Finite groups of automorphisms of Enriques surfaces and the Mathieu group M₁₂

2014/10/28 by Shigeru Mukai, Mukai, Shigeru, Hisanori Ohashi +1 · 1 citation
Mathematics · #14J28 #20D08 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1410.7535

openalex publication_date 2014/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An action of a group G on an Enriques surface S is called Mathieu if it acts on H⁰(2K_S) trivially and every element of order 2, 4 has Lefschetz number 4. A finite group G has a Mathieu action on some Enriques surface if and only if it is isomorphic to a subgroup of the symmetric group \mathfrakS₆ of degree 6 and the order |G| is not divisible by 2⁴. Explicit Mathieu actions of the three groups \mathfrak S₅, N₇₂ and \mathfrak A₆, together with non-Mathieu one of H₁₉₂, on polarized Enriques surfaces of degree 30, 18, 10 and 6, respectively, are constructed without Torelli type theorem to prove the if part.

Cited by

• On Enriques surfaces in characteristic 2 with a finite group of automorphisms

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