2006/05/08 by Fabio Perroni, Perroni, Fabio
Mathematics · #14E15 #14F45 #14N35 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14E15 #msc:14F45 #msc:14N35
paper · pdf · doi:10.48550/arxiv.math/0605207
This is a short version of my Ph.D. Thesis math.AG/0510528. Version 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a link with the classical McKay correpondence is given. International Journal of Mathematics (to appear)
openalex publication_date 2006/05/08 · arxiv created 2007/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Ruan's cohomological crepant resolution conjecture for orbifolds with transversal ADE singularities. In the An-case we compute both the Chen-Ruan cohomology ring H^*\rm CR([Y]) and the quantum corrected cohomology ring H^*(Z)(q1,...,qn). The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between H^*\rm CR([Y]) and H^*(Z)(-1) in the A1-case, verifying Ruan's conjecture. In the An-case, the family H^*(Z)(q1,...,qn) is not defined for q1=...=qn=-1. This implies that the conjecture should be slightly modified. We propose a new conjecture in the An-case which we prove in the A2-case by constructing an explicit isomorphism.