The so-called 4d SCFT/2d VOA correspondence has been the source of a fruitful interaction between physics and representation theory. One cornerstone of this interaction is the conjecture that associated varieties of VOAs arising from 4d SCFTs are isomorphic to Higgs branches, and therefore the VOAs are quasi-lisse. More recently, similar conjectures have been proposed for VOAs supported at the boundary of topologically twisted 3d N=4 theories. In this talk I will discuss these conjectures in the special case of abelian 3d N=4 gauge theories, whose Higgs branches are hypertoric varieties. I will relate some special cases to results known in the mathematical literature, and discuss various implications for free field realisations. If time will permit, I will comment on expected connections to Coulomb branches and symplectic duality.