On Non-Commutative Orbifolds of K3 Surfaces

TL;DR

This paper explores non-commutative structures in orbifolds of K3 surfaces, linking complex deformations to non-commutative algebra resolutions and discussing implications for string theory branes.

Contribution

It introduces a novel approach to non-commutative orbifolds of K3 surfaces using algebraic geometry and string theory concepts, including representations and brane fractionation.

Findings

Non-commutative algebras resolve stringy singularities.

Complex deformations correspond to non-commutative algebra resolutions.

Examples illustrate the non-commutative structure of K3 orbifolds.

Abstract

Using the algebraic geometry method of Berenstein and Leigh for the construction of the toroidal orbifold (T^2 x T^2 x T^2) / (Z_2 x Z_2) with discrete torsion and considering local K3 surfaces, we present non-commutative aspects of the orbifolds of product of K3 surfaces. In this way, the ordinary complex deformation of K3 can be identified with the resolution of stringy singularities by non-commutative algebras using crossed products. We give representations and make some comments regarding the fractionation of branes. Illustrating examples are presented.