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Chen-Ruan cohomology of ADE singularities


Perroni, F (2007). Chen-Ruan cohomology of ADE singularities. International Journal of Mathematics, 18(9):1009-1059.

Abstract

We study Ruan's cohomological crepant resolution conjecture [41] for orbifolds with transversal ADE singularities. In the An-case, we compute both the Chen–Ruan cohomology ring 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 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 (Conjecture 1.9). Finally, we prove Conjecture 1.9 in the A2-case by constructing an explicit isomorphism.

Abstract

We study Ruan's cohomological crepant resolution conjecture [41] for orbifolds with transversal ADE singularities. In the An-case, we compute both the Chen–Ruan cohomology ring 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 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 (Conjecture 1.9). Finally, we prove Conjecture 1.9 in the A2-case by constructing an explicit isomorphism.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Chen–Ruan cohomology; Ruan's conjecture; McKay correspondence
Language:English
Date:2007
Deposited On:02 Nov 2009 12:37
Last Modified:05 Apr 2016 13:23
Publisher:World Scientific Publishing
ISSN:0129-167X
Publisher DOI:https://doi.org/10.1142/S0129167X07004436
Related URLs:http://arxiv.org/abs/math.AG/0605207

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