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BIRATIONAL GEOMETRY OF SEXTIC DOUBLE SOLIDS WITH A COMPOUND 
$A_n$ SINGULARITY
Published online by Cambridge University Press: 18 September 2024
Abstract
Sextic double solids, double covers of 
$\mathbb P^3$ branched along a sextic surface, are the lowest degree Gorenstein terminal Fano 3-folds, hence are expected to behave very rigidly in terms of birational geometry. Smooth sextic double solids, and those which are 
$\mathbb Q$-factorial with ordinary double points, are known to be birationally rigid. In this paper, we study sextic double solids with an isolated compound 
$A_n$ singularity. We prove a sharp bound 
$n \leq 8$, describe models for each n explicitly, and prove that sextic double solids with 
$n> 3$ are birationally nonrigid.
MSC classification
Primary:
14J45: Fano varieties
Information
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- Article
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- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal
Footnotes
The author was supported by the Engineering and Physical Sciences Research Council (Grant No. 1820497) while in Loughborough University and the London Mathematical Society Early Career Fellowship (Grant No. ECF-1920-24) while in Imperial College London.
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