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• W2105389655 abstract "We prove a modied version of the Cohomological Crepant Resolu- tion Conjecture for the weighted projective spaces P(1; 3; 4; 4) and P(1; : : : ; 1; n). The Cohomological Crepant Resolution Conjecture, as proposed by Y. Ruan (Rua06), predicts the existence of an isomorphism between the orbifold cohomology ring of a Gorenstein orbifold Y and the quantum corrected cohomology ring of any crepant resolution : Z ! jY j of the coarse moduli space jY j of Y , when it exists. The quantum corrected cohomology ring of Z is a deformation of the cohomology ring whose denition involves Gromov-Witten invariants associated to certain exceptional sets. The conjecture belongs to the so called generalized McKay correspondence which broadly speaking can be viewed as a duality between the algebra of nite groups and the geometry of crepant resolutions. The following examples was used to verify it: the Hilbert scheme of r points on a projective surface S (see (LQ02) for r = 2, (ELQ03) and (LL) for S = P 2 r = 3, and (FG03), (QW02), (Uri05) for r general and S with numerically trivial canonical class); the Hilbert scheme of r points on a quasi-projective surface S carrying a holomorphic symplectic form (see (LQW04), (LS01) and (Vas01));" @default.
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• W2105389655 date "2007-01-01" @default.
• W2105389655 modified "2023-09-27" @default.
• W2105389655 title "ON THE COHOMOLOGICAL CREPANT RESOLUTION CONJECTURE FOR WEIGHTED PROJECTIVE SPACES" @default.
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