The Crepant Resolution Conjecture for Three-Dimensional Flags Modulo an Involution Article

Gillam, WD. (2013). The Crepant Resolution Conjecture for Three-Dimensional Flags Modulo an Involution . COMMUNICATIONS IN ALGEBRA, 41(2), 736-764. 10.1080/00927872.2011.636413

cited authors

  • Gillam, WD

authors

abstract

  • After fixing a nondegenerate bilinear form on a vector space V, we define a ℤ2-action on 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/ℤ2] agrees (up to unstable terms) with the genus zero Gromov-Witten potential function of a crepant resolution Y of the quotient scheme F/ℤ2, after setting a quantum parameter to -1, making a linear change of variables, and analytically continuing coefficients. We explicitly compute several invariants for the orbifold and the resolution, then argue that these determine the others via basic properties of Gromov-Witten invariants. © 2013 Copyright Taylor and Francis Group, LLC.

publication date

  • February 1, 2013

published in

Digital Object Identifier (DOI)

start page

  • 736

end page

  • 764

volume

  • 41

issue

  • 2