Open Access
November 2018 Gromov–Witten Invariants of the Hilbert Scheme of Two Points on a Hirzebruch Surface
Yong Fu
Michigan Math. J. 67(4): 675-713 (November 2018). DOI: 10.1307/mmj/1538532103


In Gromov–Witten theory the virtual localization method is used only when the invariant curves are isolated under a torus action. In this paper, we explore a strategy to apply the localization formula to compute the Gromov–Witten invariants by carefully choosing the related cycles to circumvent the continuous families of invariant curves when there are any. For the example of the two-pointed Hilbert scheme of Hirzebruch surface F1, we manage to compute some Gromov–Witten invariants, and then by combining with the associativity law of (small) quantum cohomology ring, we succeed in computing all 1- and 2-pointed Gromov–Witten invariants of genus 0 of the Hilbert scheme with the help of [13].


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Yong Fu. "Gromov–Witten Invariants of the Hilbert Scheme of Two Points on a Hirzebruch Surface." Michigan Math. J. 67 (4) 675 - 713, November 2018.


Received: 5 July 2013; Revised: 4 May 2018; Published: November 2018
First available in Project Euclid: 3 October 2018

zbMATH: 07056365
MathSciNet: MR3877433
Digital Object Identifier: 10.1307/mmj/1538532103

Primary: 14N35
Secondary: 53D45

Rights: Copyright © 2018 The University of Michigan

Vol.67 • No. 4 • November 2018
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