Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples

Details Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples

2006-11-17

arxiv.org/abs/math/0611550v4

Geom. Topol. 13 (2009), no.5, 2675-2744

Mathematics

Algebraic Geometry

71 pages, v2: typos corrected and references modified, v3: corrected errors in Proposition 2.9 and in Summary, v4: major revis

Scientific paper

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.

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