Open Access
2016 Ruan cohomologies of the compactifications of resolved orbifold conifolds
Song Du, Bohui Chen, Cheng-Yong Du, Xiaobin Li
Rocky Mountain J. Math. 46(3): 863-893 (2016). DOI: 10.1216/RMJ-2016-46-3-863


In this paper, we study the Ruan cohomologies of $X^s$ and $X^{sf}$, the natural compactifications of $V^s$ and $V^{sf}$, where $V^s$ and $V^{sf}$ are the two small resolutions of \[ V=\{(x,y,z,w)\mid xy-zw=0\}/\mu _r(1,-1,0,0),\quad r>1, \] the finite group quotient of the singular conifold. There is an additive isomorphism between the Chen-Ruan cohomologies $\phi :H^*_{CR}(X^s)\to H^*_{CR}(X^{sf})$. We study the three-point orbifold Gromov-Witten invariants of the exceptional curves $\Gamma ^s$ on $X^s$ and $\Gamma ^{sf}$ on $X^{sf}$ and show that the corresponding Ruan cohomology ring structures on the Chen-Ruan cohomologies of $X^s$ and $X^{sf}$, defined by these three-point functions, are isomorphic to each other under the map $\phi $ and the identification $[\Gamma ^s]\leftrightarrow -[\Gamma ^{sf}]$.


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Song Du. Bohui Chen. Cheng-Yong Du. Xiaobin Li. "Ruan cohomologies of the compactifications of resolved orbifold conifolds." Rocky Mountain J. Math. 46 (3) 863 - 893, 2016.


Published: 2016
First available in Project Euclid: 7 September 2016

zbMATH: 06628757
MathSciNet: MR3544837
Digital Object Identifier: 10.1216/RMJ-2016-46-3-863

Primary: 53D45
Secondary: 14N35

Keywords: Orbifold conifold , orbifold Gromov-Witten invariants , Ruan cohomology

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.46 • No. 3 • 2016
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