TY - JOUR
T1 - Chen-Ruan cohomology of ADE singularities
JF - International Journal of Mathematics. Volume 18, Issue 9, October 2007, Pages 1009-1059
Y1 - 2007
A1 - Fabio Perroni
KW - Chen-Ruan cohomology, Ruan\'s conjecture, McKay correspondence
AB - We study Ruan\'s \\textit{cohomological crepant resolution conjecture} for\r\norbifolds with transversal ADE singularities. In the $A_n$-case we compute both\r\nthe Chen-Ruan cohomology ring $H^*_{\\rm CR}([Y])$ and the quantum corrected\r\ncohomology ring $H^*(Z)(q_1,...,q_n)$. The former is achieved in general, the\r\nlater up to some additional, technical assumptions. We construct an explicit\r\nisomorphism between $H^*_{\\rm CR}([Y])$ and $H^*(Z)(-1)$ in the $A_1$-case,\r\nverifying Ruan\'s conjecture. In the $A_n$-case, the family\r\n$H^*(Z)(q_1,...,q_n)$ is not defined for $q_1=...=q_n=-1$. This implies that\r\nthe conjecture should be slightly modified. We propose a new conjecture in the\r\n$A_n$-case which we prove in the $A_2$-case by constructing an explicit\r\nisomorphism.
PB - SISSA
UR - http://hdl.handle.net/1963/6502
N1 - This is a short version of my Ph.D. Thesis math.AG/0510528. Version\r\n 2: chapters 2,3,4 and 5 has been rewritten using the language of groupoids; a\r\n link with the classical McKay correpondence is given. International Journal\r\n of Mathematics (to appear)
U1 - 6447
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -