BIRATIONAL GEOMETRY OF SEXTIC DOUBLE SOLIDS WITH A COMPOUND SINGULARITY

IF 0.8 2区数学 Q2 MATHEMATICS Nagoya Mathematical Journal Pub Date : 2024-09-18 DOI:10.1017/nmj.2024.17

ERIK PAEMURRU

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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.

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具有复合奇点的六分双实体的双元几何学

六次元双实体是沿六次元表面分支的 $\mathbb P^3$ 的双盖，是最低度的戈伦斯坦末端法诺 3 折叠，因此预计在双元几何方面表现得非常刚性。众所周知，光滑的六分仪双实体，以及那些具有普通双点的 $\mathbb Q$ -因子的六分仪双实体是双向刚性的。在本文中，我们研究了具有孤立复$A_n$奇点的六分双实体。我们证明了一个尖锐的约束 $n \leq 8$，明确地描述了每个 n 的模型，并证明了具有 $n> 3$ 的六分双固体是双刚性非刚性的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.

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