Fano-Mukai fourfolds of genus 10 and their automorphism groups

2021/03/22 by Yuri Prokhorov, Mikhail Zaidenberg, Prokhorov, Yuri +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2103.12167

openalex publication_date 2021/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The automorphism groups of the Fano-Mukai fourfold of genus 10 were studied in our previous paper [arXiv:1706.04926]. In particular, we found in [arXiv:1706.04926] the neutral components of these groups. In the present paper we finish the description of the discrete parts. Up to isomorphism, there are two special Fano--Mukai fourfold of genus 10 with the automorphism groups GL₂(k)\rtimesℤ/2ℤ and (\mathbbG_a×\mathbbGm)\rtimesℤ/2ℤ, respectively. For any other Fano-Mukai fourfold V of genus 10 one has Aut(V)=\mathbbG_m²\rtimes ℤ/2ℤ, except for exactly one of them with Aut(V)=\mathbbG_m²\rtimes ℤ/6 ℤ.

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