根堆栈和周期分解

Pub Date : 2024-06-15 DOI:10.1007/s00229-024-01574-y
A. Bodzenta, W. Donovan
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引用次数: 0

摘要

对于方案 X 上的有效卡蒂埃除数 D,我们可以形成一个 \({n}^{text {th}}\) 根堆栈。我们证明这个分解是 \(2n\)-periodic 的。对于(n=2),这给出了一个已知球形函子存在的纯三角证明,即沿着 D 的嵌入的推演。对于(n >2),我们找到了 Dyckerhoff 等人最近工作意义上的更高球形函子(N-球形函子和欧拉连续体的分类。arXiv:2306.13350, 2023)。我们将根栈构造的实现作为 GIT 的一种变体,这可能会引起独立的兴趣。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Root stacks and periodic decompositions

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Root stacks and periodic decompositions

For an effective Cartier divisor D on a scheme X we may form an \({n}^{\text {th}}\) root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and X. We show that this decomposition is \(2n\)-periodic. For \(n=2\) this gives a purely triangulated proof of the existence of a known spherical functor, namely the pushforward along the embedding of D. For \(n > 2\) we find a higher spherical functor in the sense of recent work of Dyckerhoff et al. (N-spherical functors and categorification of Euler’s continuants. arXiv:2306.13350, 2023). We use a realization of the root stack construction as a variation of GIT, which may be of independent interest.

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