Chen-Ruan cohomology of ADE singularities
| dc.creator | Perroni, Fabio | |
| dc.date | 2006-05-08 | |
| dc.date | 2007-01-09 | |
| dc.date.accessioned | 2026-07-07T07:39:07Z | |
| dc.date.available | 2026-07-07T07:39:07Z | |
| dc.description | We study Ruan's \textit{cohomological crepant resolution conjecture} for orbifolds with transversal ADE singularities. In the $A_n$-case we compute both the Chen-Ruan cohomology ring $H^*_{\rm CR}([Y])$ and the quantum corrected cohomology ring $H^*(Z)(q_1,...,q_n)$. 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 $A_1$-case, verifying Ruan's conjecture. In the $A_n$-case, the family $H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that the conjecture should be slightly modified. We propose a new conjecture in the $A_n$-case which we prove in the $A_2$-case by constructing an explicit isomorphism. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/math/0605207 | |
| dc.identifier | http://arxiv.org/abs/math/0605207 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121331 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E15; 14N35; 14F45 | |
| dc.title | Chen-Ruan cohomology of ADE singularities | |
| dc.type | text |