Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 56, Number 4 (2016), 873-905.
Extremal transition and quantum cohomology: Examples of toric degeneration
When a singular projective variety admits a projective crepant resolution and a smoothing , we say that and are related by extremal transition. In this article, we study a relationship between the quantum cohomology of and in some examples. For -dimensional conifold transition, a result of Li and Ruan implies that the quantum cohomology of a smoothing is isomorphic to a certain subquotient of the quantum cohomology of a resolution with the quantum variables of exceptional curves specialized to one. We observe that similar phenomena happen for toric degenerations of , , and by explicit computations.
Kyoto J. Math., Volume 56, Number 4 (2016), 873-905.
Received: 23 April 2015
Revised: 20 October 2015
Accepted: 26 November 2015
First available in Project Euclid: 7 November 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 14E30: Minimal model program (Mori theory, extremal rays)
Iritani, Hiroshi; Xiao, Jifu. Extremal transition and quantum cohomology: Examples of toric degeneration. Kyoto J. Math. 56 (2016), no. 4, 873--905. doi:10.1215/21562261-3664959. https://projecteuclid.org/euclid.kjm/1478509222