The class group of a minimal model of a quotient singularity

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-30 DOI:10.1112/blms.13100

Johannes Schmitt

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Abstract

Let $V$ be a finite-dimensional vector space over the complex numbers and let $G ⩽ SL (V)$ be a finite group. We describe the class group of a minimal model (i.e., $Q$ -factorial terminalization) of the linear quotient $V / G$ . We prove that such a class group is completely controlled by the junior elements contained in $G$ .

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商奇点最小模型的类群

让 V $V$ 是复数上的有限维向量空间，让 G ⩽ SL ( V ) $G\leqslant \operatorname{SL}(V)$ 是有限群。我们将描述线性商 V / G $V/G$ 的最小模型（即 Q $\mathbb {Q}$ -因子终结）的类群。我们证明这样的类群完全由 G $G$ 中包含的初等元素控制。

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