Non-commutative Toric Varieties

TL;DR

This paper introduces non-commutative toric varieties, extending LVM-theory for irrational cases and using diffeology to model their moduli spaces, advancing the understanding of non-commutative geometric structures.

Contribution

It presents a new class of non-commutative spaces called non-commutative toric varieties and develops their theoretical framework using extended LVM-theory and diffeology.

Findings

Defined non-commutative toric varieties and described their properties

Extended LVM-theory to irrational cases for non-commutative spaces

Used diffeology to model moduli spaces of these varieties

Abstract

In this note we introduce a new family of non-commutative spaces that we call non-commutative toric varieties and we describe some of their main properties. The main technical tool in this investigation is a natural extension of LVM-theory for the irrational case. In order to introduce the moduli space of (non-commutative) toric varieties we use variations on the notion of diffeology as models for non-commutative spaces.