Birational geometry of sextic double solids with a compound $A_n$ singularity
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2021
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916540338667520 |
|---|---|
| author | Paemurru, Erik |
| author_facet | Paemurru, Erik |
| contents | Sextic double solids, double covers of $\mathbb P^3$ branched along a sextic surface, are the lowest degree Gorenstein 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 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 non-rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_00501 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Birational geometry of sextic double solids with a compound $A_n$ singularity Paemurru, Erik Algebraic Geometry 14J45 (Primary) 14J30, 14J17, 14E30, 14E05 (Secondary) Sextic double solids, double covers of $\mathbb P^3$ branched along a sextic surface, are the lowest degree Gorenstein 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 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 non-rigid. |
| title | Birational geometry of sextic double solids with a compound $A_n$ singularity |
| topic | Algebraic Geometry 14J45 (Primary) 14J30, 14J17, 14E30, 14E05 (Secondary) |
| url | https://arxiv.org/abs/2101.00501 |