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arXiv · 2210.03227

Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces

Benjamin Gammage·Maxim Jeffs
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Abstract

We prove that homological mirror symmetry for very affine hypersurfaces respects certain natural symplectic operations (as functors between partially wrapped Fukaya categories), verifying conjectures of Auroux. These conjectures concern compatibility between mirror symmetry for a very affine hypersurface and its complement, itself also a very affine hypersurface. We find that the complement of a very affine hypersurface has in fact two natural mirrors, one of which is a derived scheme. These two mirrors are related via a non-geometric equivalence mediated by Kn\"orrer periodicity; Auroux's conjectures require some modification to take this into account. Our proof also introduces new techniques for presenting Liouville manifolds as gluings of Liouville sectors.

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Benjamin Gammage, Maxim Jeffs. 2022-10-06. Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces. https://doi.org/10.1112/topo.70012

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