当前位置: X-MOL 学术Adv. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Singularity categories via the derived quotient
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-02-09 , DOI: 10.1016/j.aim.2021.107631
Matt Booth

Given a noncommutative partial resolution A=EndR(RM) of a Gorenstein singularity R, we show that the relative singularity category ΔR(A) of Kalck–Yang is controlled by a certain connective dga A/LAeA, the derived quotient of Braun–Chuang–Lazarev. We think of A/LAeA as a kind of ‘derived exceptional locus’ of the partial resolution A, as we show that it can be thought of as the universal dga fitting into a suitable recollement. This theoretical result has geometric consequences. When R is an isolated hypersurface singularity, it follows that the singularity category Dsg(R) is determined completely by A/LAeA, even when A has infinite global dimension. Thus our derived contraction algebra classifies threefold flops, even those XSpec(R) where X has only terminal singularities. This gives a solution to the strongest form of the derived Donovan–Wemyss conjecture, which we further show is the best possible classification result in this singular setting.



中文翻译:

通过导出商的奇异性类别

给出非交换部分分辨率 一个=结束[R[R中号Gorenstein奇点R的方程,我们证明了相对奇点类别Δ[R一个 Kalck–Yang的控制由某个结缔组织dga控制 一个/大号一个Ë一个,即Braun–Chuang–Lazarev的导出商。我们想到一个/大号一个Ë一个作为部分分辨率A的一种“派生例外轨迹” ,正如我们所展示的,它可以被认为是适合于适当折衷的通用dga。该理论结果具有几何后果。当R是一个孤立的超曲面奇点时,奇点类别dg[R 完全取决于 一个/大号一个Ë一个,即使A具有无限的全局维。因此,我们得出的收缩代数将三级触发器分类,即使是那些X规格[R其中X仅具有末端奇异点。这为派生的Donovan-Wemyss猜想的最强形式提供了一种解决方案,我们进一步证明了在这种奇异设置下最好的分类结果。

更新日期:2021-02-09
down
wechat
bug