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Homological mirror symmetry for higher-dimensional pairs of pants
Published online by Cambridge University Press: 18 June 2020
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
$\mathbb{CP}^{n}$, for
$k\geqslant n$, 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
$x_{1}x_{2}\ldots x_{n+1}=0$. By localizing, we deduce that the (fully) wrapped Fukaya category of the
$n$-dimensional pair of pants is equivalent to the derived category of
$x_{1}x_{2}\ldots x_{n+1}=0$. We also prove similar equivalences for finite abelian covers of the
$n$-dimensional pair of pants.
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- Research Article
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- © The Authors 2020
References
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