Kähler Moduli Space of a D-Brane at Orbifold Singularities

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 ${\Bbb C}^d/Γ$ using the theory of toric quotients. This approach elucidates the structure of the Kähler moduli space associated with the problem. As an application, we compute the toric data of the $Γ$-Hilbert scheme.