Xiaojun Chen

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math.AG2025

Singularity categories and singular loci of certain quotient singularities

Xiaojun Chen, Jieheng Zeng

Let $V$ be a finite dimensional $k$ -vector space, where $k$ is an algebraic closed field of characteristic zero. Let $G \subseteq SL (V)$ be a finite abelian group, and den…

math.AG2025

On the graded singularity category of Abelian quotient singularities, I. Smooth categorical compactification

Xiaojun Chen, Jieheng Zeng

Given a singularity which is the quotient of an affine space $V$ by a finite Abelian group $G \subseteq SL (V)$ , we study the DG enhancement $\mathcal{D}^{b}(\mathrm{tails}…