Article

Tilting objects in graded singularity categories of certain toric Gorenstein singularities

Xiaojun ChenNew Uzbekistan University, Tashkent, UzbekistanL. LiuZhejiang University of Science and Technology, Hangzhou, P. R. ChinaJieheng ZengHunan Normal University, Changsha, P. R. China

Journal of Noncommutative Geometryjournal2026

ABI

Abstract

We study a class of Gorenstein isolated singularities which are the quotients of generic and unimodular representations of the one-dimensional torus, or of the product of the one-dimensional torus with a finite abelian group. Based on the works of Špenko and van den Bergh [Invent. Math. 210 (2017), 3–67] and Mori and Ueyama [Adv. Math. 297 (2016), 54–92], we show that the graded singularity categories of these varieties admit tilting objects, and hence are triangulated equivalent to the perfect categories of some finite-dimensional algebras.

Topics

Algebraic structures and combinatorial models Advanced Combinatorial Mathematics Advanced Algebra and Geometry

Identifiers

DOI: 10.4171/jncg/665

Citations and references

Cited by 00 references

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