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TITLE Homological mirror symmetry for higher-dimensional pairs of pants
KIAS AUTHORS Polishchuk, Alexander
JOURNAL COMPOSITIO MATHEMATICA, 2020
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ABSTRACT 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 CPn, 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 CPn (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 then-dimensional pair of 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 then-dimensional pair of pants.
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