Work

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

Year: 2024

Type: article

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 nongeometric equivalence mediated by Knörrer 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.

Source: Journal of Topology

DOI: 10.1112/topo.70012

Authors: Benjamin Gammage, Maxim Jeffs

Institutions: Harvard University, University of Cambridge

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Simons Foundation

Awards: G188276817, PostDoctoral Research Fellowship, Admissible Lagrangians, Fukaya categories, and homological mirror symmetry., Partially Wrapped Fukaya Categories and Functoriality in Mirror Symmetry