The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution
Abstract
After fixing a non-degenerate bilinear form on a vector space V we define an involution of the manifold of flags F in V by taking a flag to its orthogonal complement. When V is of dimension 3 we check that the Crepant Resolution Conjecture of J. Bryan and T. Graber holds: the genus zero (orbifold) Gromov-Witten potential function of [F / Z_2] agrees (up to unstable terms) with the genus zero Gromov-Witten potential function of a crepant resolution Y of the quotient scheme F / Z_2, after setting a quantum parameter to -1, making a linear change of variables, and analytically continuing coefficients. The crepant resolution Y (a hypersurface in the Hilbert scheme Hilb^2 P^2) is the projectivization of a novel rank 2 vector bundle over P^2.
Cite
@article{arxiv.0708.0842,
title = {The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution},
author = {W. D. Gillam},
journal= {arXiv preprint arXiv:0708.0842},
year = {2007}
}
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23 pages