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2020 Higher genus relative and orbifold Gromov–Witten invariants
Hsian-Hua Tseng, Fenglong You
Geom. Topol. 24(6): 2749-2779 (2020). DOI: 10.2140/gt.2020.24.2749

Abstract

Given a smooth projective variety X and a smooth divisor DX, we study relative Gromov–Witten invariants of (X,D) and the corresponding orbifold Gromov–Witten invariants of the r th root stack XD,r. For sufficiently large r, we prove that orbifold Gromov–Witten invariants of XD,r are polynomials in r. Moreover, higher-genus relative Gromov–Witten invariants of (X,D) are exactly the constant terms of the corresponding higher-genus orbifold Gromov–Witten invariants of XD,r. We also provide a new proof for the equality between genus-zero relative and orbifold Gromov–Witten invariants, originally proved by Abramovich, Cadman and Wise (2017). When r is sufficiently large and X=C is a curve, we prove that stationary relative invariants of C are equal to the stationary orbifold invariants in all genera.

Citation

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Hsian-Hua Tseng. Fenglong You. "Higher genus relative and orbifold Gromov–Witten invariants." Geom. Topol. 24 (6) 2749 - 2779, 2020. https://doi.org/10.2140/gt.2020.24.2749

Information

Received: 13 September 2018; Revised: 4 December 2019; Accepted: 2 January 2020; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194303
Digital Object Identifier: 10.2140/gt.2020.24.2749

Subjects:
Primary: 14N35
Secondary: 14H10

Keywords: degeneration , relative Gromov–Witten invariants , root stacks , virtual localization

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.24 • No. 6 • 2020
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