Compactifying the Parameter Space for the Quantum Multiplication for Hypertoric Varieties

Abstract: In this paper, we will be studying the parameter space for the quantum multiplication for hypertoric varieties. The operation of quantum multiplication for hypertoric varieties has an explicit formulation which is given by McBreen and Shenfeld. In particular, this multiplication depends on a parameter which lives in the complement of a toric arrangement. Following a paper of deConcini and Gaiffi, I will define a compactification of this parameter space and show how the quantum multiplication can be extended to this compactification.