Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent C\^ot\'e and Justin Hilburn)

Abstract

In this paper, we prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories by promoting our result to an equivalence of perverse schobers. We prove our equivalence by matching holomorphic Lagrangian skeleta, on the A-model side, with non-commutative resolutions on the B-model side. The hyperk\"ahler geometry of these spaces provides each category with a natural t-structure, which helps clarify SYZ duality in a hyperk\"ahler context. Our results are a prototype for mirror symmetry statements relating pairs of K-theoretic Coulomb branches.