K\"ahler Moduli Space of a D-Brane at Orbifold Singularities

TL;DR

This paper introduces a systematic method using toric quotients to analyze the Kähler moduli space of D-branes at orbifold singularities on Calabi-Yau manifolds, with applications to computing toric data of the $ ext{Gamma}$-Hilbert scheme.

Contribution

It develops a new approach to analyze the configuration space of D-branes at orbifold singularities using toric quotients, providing insights into the Kähler moduli space.

Findings

Elucidates the structure of the Kähler moduli space for D-branes at orbifold points.

Computes the toric data of the $ ext{Gamma}$-Hilbert scheme.

Provides a systematic method applicable to Calabi-Yau orbifolds.

Abstract

We develop a method to analyze systematically the configuration space of a D-brane localized at the orbifold singular point of a Calabi--Yau $d$-fold of the form ${\Bbb C}^d/\Gamma$ using the theory of toric quotients. This approach elucidates the structure of the K\"ahler moduli space associated with the problem. As an application, we compute the toric data of the $\Gamma$-Hilbert scheme.