Paemurru, Erik. (2021) Birational geometry of sextic double solids with a compound $A_n$ singularity. Preprints Fachbereich Mathematik, 2021 (02).

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Abstract
Sextic double solids, double covers of $\mathbb P^3$ branched along a sextic surface, are the lowest degree Gorenstein Fano 3folds, 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 article, 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.
Faculties and Departments:  12 Special Collections > Preprints Fachbereich Mathematik 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc) 

UniBasel Contributors:  Paemurru, Erik 
Item Type:  Preprint 
Publisher:  Universität Basel 
Language:  English 
edoc DOI:  
Last Modified:  01 Feb 2021 19:16 
Deposited On:  01 Feb 2021 19:16 
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