On the Crepant Resolution Conjecture in the Local Case

Details On the Crepant Resolution Conjecture in the Local Case On the Crepant Resolution Conjecture in the Local Case

2008-10-13

arxiv.org/abs/0810.2200v1

Mathematics

Algebraic Geometry

27 pages. This is a substantially revised and shortened version of my preprint "Wall-Crossings in Toric Gromov-Witten Theory I

Scientific paper

10.1007/s00220-008-0715-y

In this paper we analyze four examples of birational transformations between local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial resolution, 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.

Affiliated with

Also associated with

No associations

Rating

On the Crepant Resolution Conjecture in the Local Case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Crepant Resolution Conjecture in the Local Case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Crepant Resolution Conjecture in the Local Case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-720158