## Geometry & Topology

### Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples

#### Abstract

Let $X$ be a Gorenstein orbifold with projective coarse moduli space $X$ 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.

#### Article information

Source
Geom. Topol., Volume 13, Number 5 (2009), 2675-2744.

Dates
Revised: 21 October 2008
Accepted: 25 May 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800321

Digital Object Identifier
doi:10.2140/gt.2009.13.2675

Mathematical Reviews number (MathSciNet)
MR2529944

Zentralblatt MATH identifier
1184.53086

#### Citation

Coates, Tom; Iritani, Hiroshi; Tseng, Hsian-Hua. Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples. Geom. Topol. 13 (2009), no. 5, 2675--2744. doi:10.2140/gt.2009.13.2675. https://projecteuclid.org/euclid.gt/1513800321

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