The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: After fixing a non-degenerate bilinear form on a vector space V we define aninvolution of the manifold of flags F in V by taking a flag to its orthogonalcomplement. When V is of dimension 3 we check that the Crepant ResolutionConjecture of J. Bryan and T. Graber holds: the genus zero orbifoldGromov-Witten potential function of F - Z 2 agrees up to unstable termswith the genus zero Gromov-Witten potential function of a crepant resolution Yof the quotient scheme F - Z 2, after setting a quantum parameter to -1, makinga linear change of variables, and analytically continuing coefficients. Thecrepant resolution Y a hypersurface in the Hilbert scheme Hilb^2 P^2 is theprojectivization of a novel rank 2 vector bundle over P^2.



Author: W. D. Gillam

Source: https://arxiv.org/







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