Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbifold Cohomology of ADE-singularities   We study Ruan's "cohomological crepant resolution conjecture" (see
math.AG/0108195) for orbifolds with transversal ADE singularities. Let [Y] be
such an orbifold, Y its coarse moduli space and Z the crepant resolution of Y.
Following Ruan [math.AG/0108195], we have a deformation of the cohomology ring
H^*(Z) using some Gromov-Witten invariants of Z. The resulting family of rings
will be denoted by H^*(Z)(q_1,...,q_n), where q_1,...,q_n are complex
parameters. In the A_n case we compute both the orbifold cohomology ring
H^*_{orb}([Y]) and the family H^*(Z)(q_1,...,q_n). The former is achieved in
general, the later up to an explicit conjecture on the Gromov-Witten invariants
which is verified under additional, technical assumptions. We construct an
explicit isomorphism between H^*_{orb}([Y]) and H^*(Z)(-1) in the A_1 case,
verifying Ruan's conjecture. In the A_2 case, the family H^*(q_1,q_2) is not
defined for q_1=q_2=-1, so the conjecture should be slightly modified. However
we give an explicit isomorphism between H^*_{orb}([Y]) and H^*(Z)(q_1,q_2) with
q_1=q_2 be a primitive third root of the unity, thus proving a slightly
modified version of Ruan's conjecture. It is natural to conjecture that, in the
A_n case, H^*_{orb}([Y]) is isomorphic to H^*(Z)(q_1,...,q_n) with q_1=...=q_n
be a primitive (n+1)-th root of the unity.

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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph