The moduli stack of affine stable toric varieties

TL;DR

This paper describes the moduli space of affine stable toric T-varieties over an irreducible affine T-variety as a quotient stack of an open subscheme in a toric Hilbert scheme, providing a geometric classification framework.

Contribution

It introduces a new description of the moduli space of affine stable toric T-varieties as a quotient stack, linking it to toric Hilbert schemes.

Findings

Moduli space characterized as a quotient stack

Open subscheme in a toric Hilbert scheme identified

Provides a geometric framework for classifying affine stable toric varieties

Abstract

Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient stack of an open subscheme in a certain toric Hilbert scheme under the action of a torus.