English

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

Algebraic Geometry 2007-08-08 v1

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.

Keywords

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}
}

Comments

23 pages

R2 v1 2026-06-21T09:05:17.843Z