Communications in Analysis and Geometry

Volume 21 (2013)

Number 3

An example of Crepant Resolution Conjecture in two steps

Pages: 527 – 539

DOI: http://dx.doi.org/10.4310/CAG.2013.v21.n3.a3

Authors

Renzo Cavalieri (Department of Mathematics, Colorado State University, U.S.A.)

Gueorgui Todorov (Princeton University, New Jersey, U.S.A.)

Abstract

We study the relation among the genus $0$ Gromov-Witten theories of the three spaces $\mathcal{X}\leftarrow\mathcal{Z}\leftarrow Y$, where $\mathcal{X}=[\mathbb{C}^2/ \mathbb{Z}_3]$, $\mathcal{Z}$ is obtained by a weighted blow-up at the stacky point of $\mathcal{X}$, and $Y$ is the crepant resolution of the $A_2$ singularity. We formulate and verify a statement generalizing the Crepant Resolution Conjecture of Bryan and Graber, that we call the Crepant Partial Resolution Conjecture.

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