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Tilting objects in graded singularity categories of certain toric Gorenstein singularities

  • Xiaojun Chen

    Sichuan University, Chengdu, P. R. China; New Uzbekistan University, Tashkent, Uzbekistan

  • Leilei Liu

    Zhejiang University of Science and Technology, Hangzhou, P. R. China

  • Jieheng Zeng

    Hunan Normal University, Changsha, P. R. China
Tilting objects in graded singularity categories of certain toric Gorenstein singularities cover

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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.

Cite this article

Xiaojun Chen, Leilei Liu, Jieheng Zeng, Tilting objects in graded singularity categories of certain toric Gorenstein singularities. J. Noncommut. Geom. (2026), published online first

DOI 10.4171/JNCG/665