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December 2016 Extremal transition and quantum cohomology: Examples of toric degeneration
Hiroshi Iritani, Jifu Xiao
Kyoto J. Math. 56(4): 873-905 (December 2016). DOI: 10.1215/21562261-3664959

Abstract

When a singular projective variety Xsing admits a projective crepant resolution Xres and a smoothing Xsm, we say that Xres and Xsm are related by extremal transition. In this article, we study a relationship between the quantum cohomology of Xres and Xsm in some examples. For 3-dimensional conifold transition, a result of Li and Ruan implies that the quantum cohomology of a smoothing Xsm is isomorphic to a certain subquotient of the quantum cohomology of a resolution Xres with the quantum variables of exceptional curves specialized to one. We observe that similar phenomena happen for toric degenerations of Fl(1,2,3), Gr(2,4), and Gr(2,5) by explicit computations.

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Hiroshi Iritani. Jifu Xiao. "Extremal transition and quantum cohomology: Examples of toric degeneration." Kyoto J. Math. 56 (4) 873 - 905, December 2016. https://doi.org/10.1215/21562261-3664959

Information

Received: 23 April 2015; Revised: 20 October 2015; Accepted: 26 November 2015; Published: December 2016
First available in Project Euclid: 7 November 2016

zbMATH: 1360.14132
MathSciNet: MR3568645
Digital Object Identifier: 10.1215/21562261-3664959

Subjects:
Primary: 14N35
Secondary: 14E30, 53D45

Rights: Copyright © 2016 Kyoto University

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Vol.56 • No. 4 • December 2016
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