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arXiv · 2508.04367

Automorphism groups and cylindricity of weighted hypersurface Fano threefolds

In-Kyun Kim·Takashi Kishimoto·Joonyeong Won
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Abstract

It is well known that there are totally 130 deformation families of quasi-smooth terminal weighted hypersurface Fano threefolds and all members belonging to 95 families of Fano indices one are birationally rigid. Among remaining $35$ families, $15$ families have the property that general members are irrational, in particular, any of them has a finite automorphism group and is not cylindrical. In the present paper, we will observe the cylindricity and the full automorphism groups of every member in the remaining $20$ families. Moreover, we deal with the cylindricity of their forms.

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In-Kyun Kim, Takashi Kishimoto, Joonyeong Won. 2025-08-06. Automorphism groups and cylindricity of weighted hypersurface Fano threefolds. https://arxiv.org/abs/2508.04367

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