Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples
arXiv:0804.2592
Abstract
In this paper we analyze six examples of birational transformations between toric orbifolds: three crepant resolutions, two crepant partial resolutions, and a flop. We study the effect of these transformations on genus-zero Gromov-Witten invariants, proving the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of the Crepant Resolution Conjecture may also hold for more general crepant birational transformations. They also suggest that Ruan's original Crepant Resolution Conjecture should be modified, by including appropriate "quantum corrections", and that there is no straightforward generalization of either Ruan's original Conjecture or the Cohomological Crepant Resolution Conjecture to the case of crepant partial resolutions. Our methods are based on mirror symmetry for toric orbifolds.
37 pages
References in corpus (14)
- A New Cohomology Theory for Orbifold
- Computing Genus-Zero Twisted Gromov-Witten Invariants
- Hypergeometric functions and mirror symmetry in toric varieties
- Quantum D-modules and generalized mirror transformations
- Quantum Cohomology and Crepant Resolutions: A Conjecture
- Real and integral structures in quantum cohomology I: toric orbifolds
- The Crepant Resolution Conjecture for Type A Surface Singularities
- Hurwitz-Hodge Integrals, the E6 and D4 root systems, and the Crepant Resolution Conjecture
- The Quantum Orbifold Cohomology of Weighted Projective Spaces
- Gerby Localization, Z_3-Hodge Integrals and the GW Theory of C^3/Z_3
- Crepant resolutions of weighted projective spaces and quantum deformations
- The cohomological crepant resolution conjecture for P(1,3,4,4)
- The genus zero Gromov-Witten invariants of [Sym^2 P^2]
- The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution
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- Equivariant mirror symmetry for the weighted projective line