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Gromov–Witten theory
of Hilbert schemes of points on elliptic surfaces with
multiple fibers
Mazen M. Alhwaimel and Zhenbo Qin |
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Vol. 339 (2025), No. 1, 1–21
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Abstract |
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We study the Gromov–Witten theory of Hilbert schemes of points on elliptic surfaces with multiple fibers. We prove a vanishing theorem for the Gromov–Witten invariants of these Hilbert schemes, and compute the exceptional genus-0 case for the Hilbert schemes of two points on elliptic surfaces with exactly one multiple fiber. The strategy is to use the theory of cosection localization and compute a certain obstruction sheaf. |
Keywords
Gromov–Witten invariant, Hilbert scheme, cosection
localization, elliptic surface, stable map
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Mathematical Subject Classification
Primary: 14C05, 14N35
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Milestones
Received: 20 September 2024
Revised: 4 July 2025
Accepted: 14 August 2025
Published: 1 September 2025
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Authors |
| Mazen M. Alhwaimel | |
| Department of Mathematics College of Science, Qassim University Buraydah 51452 Saudi Arabia |
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| Zhenbo Qin | |
| Department of Mathematics University of Missouri Columbia, MO 65211 United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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