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Homological mirror symmetry for higher-dimensional pairs of pants

Research output: Contribution to journalArticle

Yanki Lekili, Alexander Polishchuk

Original languageEnglish
Pages (from-to)1310-1347
Number of pages38
JournalCOMPOSITIO MATHEMATICA
Volume156
Issue number7
Early online date18 Jun 2020
DOIs
Accepted/In press8 Jan 2020
E-pub ahead of print18 Jun 2020
Published1 Jul 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 generic hyperplanes in, for, 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 generic hyperplanes in (-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. By localizing, we deduce that the (fully) wrapped Fukaya category of the-dimensional pair of pants is equivalent to the derived category of. We also prove similar equivalences for finite abelian covers of the-dimensional pair of pants.

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