Singularity categories and singular loci of certain quotient singularities
Xiaojun Chen, Jieheng Zeng

TL;DR
This paper demonstrates that the singularity category of certain quotient singularities precisely captures the reduced singular locus of their spectrum, linking categorical and geometric aspects of these singularities.
Contribution
It establishes a direct connection between the singularity category and the reduced singular locus for quotient singularities arising from finite abelian groups in characteristic zero.
Findings
Singularity category recovers the reduced singular locus.
Provides a categorical perspective on quotient singularities.
Links algebraic and geometric properties of singularities.
Abstract
Let be a finite dimensional -vector space, where is an algebraic closed field of characteristic zero. Let be a finite abelian group, and denote by the -invariant subring of the polynomial ring . It is shown that the singularity category recovers the reduced singular locus of .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra
