Crepant Resolutions of C^n/A_1(n) and Flops of n-Folds for n = 4,5

Abstract

In this article, we determine the explicit toric variety structure of \(\hl^{A_1(n)}(\CZ^n)\) for \(n=4,5\), where \(A_1(n)\) is the special diagonal group of all order 2 elements. Through the toric data of \(\hl^{A_1(n)}(\CZ^n)\), we obtain certain toric crepant resolutions of \(\CZ^n/A_1(n)\), and the different crepant resolutions are connected by flops of \(n\)-folds for \(n=4,5\).