The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution

Details The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution

2007-08-06

arxiv.org/abs/0708.0842v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

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.

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