Using Auroux's description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^n$, for $k \geq n$, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In the case of the complement of $(n+2)$-generic hyperplanes in $\mathbb{C}P^n$ ($n$-dimensional pair-of-pants), we show that our partial wrapped Fukaya category is equivalent to a certain categorical resolution of the derived category of the singular affine variety $x_1x_2..x_{n+1}=0$. By localizing, we deduce that the (fully) wrapped Fukaya category of $n$-dimensional pants is equivalent to the derived category of $x_1x_2...x_{n+1}=0$. We also prove similar equivalences for finite abelian covers of the $n$-dimensional pair-of-pants.

中文翻译：

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高维裤子的同调镜像对称

使用 Auroux 对穿孔曲面对称乘积的 Fukaya 范畴的描述，我们计算 $\mathbb{CP}^n$ 中 $k+1$ 泛型超平面的补集的部分包裹 Fukaya 范畴，对于 $k\geq n$，关于对象生成集的自同态代数方面的某些停止。选择停止点，以便生成的代数是正式的。在 $\mathbb{C}P^n$（$n$-维对裤）中 $(n+2)$-泛型超平面的补集的情况下，我们证明我们的部分包裹的 Fukaya 类别是等价于奇异仿射变体 $x_1x_2..x_{n+1}=0$ 的派生范畴的某个分类分辨率。通过本地化，我们推断出$n$维裤子的（完全）包裹的Fukaya类别等价于$x_1x_2...x_{n+1}=0$的派生类别。