具有复合奇点的六分双实体的双元几何学

Pub Date : 2024-09-18 DOI:10.1017/nmj.2024.17
ERIK PAEMURRU
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引用次数: 0

摘要

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。
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BIRATIONAL GEOMETRY OF SEXTIC DOUBLE SOLIDS WITH A COMPOUND SINGULARITY
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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