论文标题
git的变化和拉格朗日骨骼的变化II：准对称情况
Variation of GIT and Variation of Lagrangian Skeletons II: Quasi-Symmetric Case
论文作者
论文摘要
考虑$（\ mathbb {c}^*）^k $作用于$ \ mathbb {c}^n $满足某些“ Quasi-Metressric”条件，该条件会产生一类曲折的Calabi-yau git商堆栈。使用$ coh（[\ mathbb {c}^n /（\ mathbb {c}^*）^k]）$的子类别是由线捆生成的，其权重在某些称为“魔术窗口”，Halpern-Leistner和Sam的界限内的捆绑包中，给出了均等的分类，以构建均等的coherents Sheaiervors coherent Sheaiers seperiatients of Equivalence。我们将相干构造的对应物应用于魔术窗口，并在$ \ Mathbb {r}^{n-k}中获得Lagrangian骨架的非特征变形，由$ \ Mathbb {r}^k $参数化的参数化。此外，通过在$ \ mathbb {r}^k $中翻译魔术窗口，我们获得了$ \ m \ m i \ m}^k \ times \ times \ m}^k \ setminus \ setMinus \ natercal \ mathcal {d} $的普通骨架的通用骨架，以$ \ m m iester $ \ mathcal $ \ mathcal}诱导$ \ mathbb {r}^k \ times \ mathbb {r}^k \ setMinus \ mathcal {d} $上的类别的本地系统。我们还将结果连接到Špenko和van den Bergh确定的合理的Schober结构。
Consider $(\mathbb{C}^*)^k$ acting on $\mathbb{C}^N$ satisfying certain 'quasi-symmetric' condition which produces a class of toric Calabi-Yau GIT quotient stacks. Using subcategories of $Coh([\mathbb{C}^N / (\mathbb{C}^*)^k])$ generated by line bundles whose weights are inside certain zonotope called the 'magic window', Halpern-Leistner and Sam give a combinatorial construction of equivalences between derived categories of coherent sheaves for various GIT quotients. We apply the coherent-constructible correspondence for toric varieties to the magic windows and obtain a non-characteristic deformation of Lagrangian skeletons in $\mathbb{R}^{N-k}$ parameterized by $\mathbb{R}^k$, exhibiting derived equivalences between A-models of the various phases. Moreover, by translating the magic window zonotope in $\mathbb{R}^k$, we obtain a universal skeleton over $\mathbb{R}^k \times \mathbb{R}^k \setminus \mathcal{D}$ for some fattening of hyperplane arrangements $\mathcal{D}$, and we show that the the universal skeleton induces a local system of categories over $\mathbb{R}^k \times \mathbb{R}^k \setminus \mathcal{D}$. We also connect our results to the perverse schober structure identified by Špenko and Van den Bergh.
