Crepant Resolutions of Cⁿ/A₁(n) and Flops of n-Folds for n = 4,5

2002/08/31 by Li Chiang, Shi-shyr Roan
Mathematics · #math.AG #msc:14M25 #msc:14J17 #msc:20C33 #msc:13P10

paper · pdf

published as "Calabi-Yau varieties and mirror symmetry", eds. N. Yui and J. D. Lewis, Fields Institute Comm. 38, 2003, Amer. Math. Soc. 27-41 ; math.AG/0208052 · 15 pages, 8 figures

arxiv created 2003/11/29 · arxiv updated 2009/11/30

Abstract

In this article, we determine the explicit toric variety structure of \hl^A₁(n)(\CZⁿ) for n=4,5, where A₁(n) is the special diagonal group of all order 2 elements. Through the toric data of \hl^A₁(n)(\CZⁿ), we obtain certain toric crepant resolutions of \CZⁿ/A₁(n), and the different crepant resolutions are connected by flops of n-folds for n=4,5.

Related

• Exceptional Collections for Toric Fano Fourfolds
• Exceptional Collections for Toric Fano Fivefolds
• Crepant resolutions and brane tilings II: Tilting bundles
• Crepant resolution conjecture for ℂ⁵/ℤ₅
• Non-commutative crepant resolutions for some toric singularities II