The Hamiltonian reduction of hypertoric mirror symmetry

TL;DR

This paper proves a theorem showing that the Fukaya category behaves compatibly with Hamiltonian reduction in the setting of multiplicative hypertoric varieties, advancing understanding of mirror symmetry.

Contribution

It establishes a new 'Fukaya category commutes with reduction' theorem for Hamiltonian torus actions on multiplicative hypertoric varieties.

Findings

Fukaya category commutes with reduction in this setting

Provides new insights into hypertoric mirror symmetry

Advances the mathematical framework connecting symplectic geometry and mirror symmetry

Abstract

We give a `Fukaya category commutes with reduction' theorem for the Hamiltonian torus action on a multiplicative hypertoric variety.