Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples
Abstract
Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov--Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and Bryan--Graber, and prove our conjecture when X = P(1,1,2) and X = P(1,1,1,3). As a consequence, we see that the original form of the Bryan--Graber Conjecture holds for P(1,1,2) but is probably false for P(1,1,1,3). Our methods are based on mirror symmetry for toric orbifolds.
Keywords
Cite
@article{arxiv.math/0611550,
title = {Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples},
author = {Tom Coates and Hiroshi Iritani and Hsian-Hua Tseng},
journal= {arXiv preprint arXiv:math/0611550},
year = {2014}
}
Comments
71 pages, v2: typos corrected and references modified, v3: corrected errors in Proposition 2.9 and in Summary, v4: major revision, exposition unified from a viewpoint of VSHS, many signpostings for the logical structure; the authorship has changed, with Alessio Corti withdrawing