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Homological mirror symmetry for higher-dimensional pairs of pants
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 ℂℙ^n, for k≥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 ℂP^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_1 x_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_1 x_2 ... x_{n+1}=0. We also prove similar equivalences for finite abelian covers of the n-dimensional pair-of-pants.