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Fano–Mukai fourfolds of genus 10 and their automorphism groups

European Journal of Mathematics. 2022. Vol. 8. No. 2. P. 561–572.
Prokhorov Y., Zaidenberg M.

The automorphism groups of the Fano–Mukai fourfold of genus 10 were studied in our previous paper (Prokhorov and Zaidenberg in Eur J Math 4(3):1197–1263, 2018). In particular, we found the neutral components of these groups. In the present paper we finish the description of the discrete parts. Up to isomorphism, there are three special Fano–Mukai fourfold of genus 10 with the automorphism groups GL2(𝕜)⋊ℤ/2ℤGL2(k)⋊Z/2Z, (𝔾a×𝔾m)⋊ℤ/2ℤ(Ga×Gm)⋊Z/2Zand 𝔾2m⋊ℤ/6ℤGm2⋊Z/6Z, respectively. For any other Fano–Mukai fourfold V of genus 10 one has Aut(𝑉)=𝔾2m⋊ℤ/2ℤAut(V)=Gm2⋊Z/2Z.

Research target: Mathematics
Language: English
DOI
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Keywords: automorphism groupCubic scrollFano–Mukai fourfold
Publication based on the results of:
Algebraic varieties from the point of view of derived categories, homological algebra, special holonomy metrics and classical algebraic geometry (2022)
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