Elliptic Hypertoric Varieties

TL;DR

This paper introduces elliptic hypertoric varieties, extending hypertoric concepts into the elliptic setting, and proves an elliptic version of the Hikita conjecture relating these varieties to equivariant elliptic cohomology.

Contribution

It presents the first elliptic analogue of hypertoric varieties and establishes a new elliptic Hikita conjecture linking these varieties to elliptic cohomology.

Findings

Defined elliptic hypertoric varieties.

Proved elliptic Hikita conjecture.

Connected elliptic varieties to equivariant elliptic cohomology.

Abstract

We introduce elliptic hypertoric varieties, which is an elliptic analogue of hypertoric varieties and multiplicative hypertoric varieties. We also prove an elliptic version of Hikita conjecture, which relates elliptic (resp. additive and mulitplicative) hypertoric varieties to the equivariant elliptic cohomology (resp. ordinary cohomology and K-theory) of their 3d mirror hypertoric varieties.