Geodesic
Extremal Gromov-Witten invariants of the Hilbert scheme of $3$ Points
Forum of Mathematics, Sigma, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

We determine all the extremal Gromov-Witten invariants of the Hilbert scheme of $3$ points on a smooth projective complex surface. Our result for the genus-$1$ case verifies a conjecture that we propose for the genus-$1$ extremal Gromov-Witten invariant of the Hilbert scheme of n points with n being arbitrary. The main ideas in the proofs are to use geometric arguments involving the cosection localization theory of Kiem and J. Li [17, 23], algebraic manipulations related to the Heisenberg operators of Grojnowski [13] and Nakajima [34], and the virtual localization formulas of Gromov-Witten theory [12, 20, 30]. 
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     author = {Jianxun Hu and Zhenbo Qin},
     title = {Extremal {Gromov-Witten} invariants of the {Hilbert} scheme of $3$ {Points}},
     journal = {Forum of Mathematics, Sigma},
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Jianxun Hu; Zhenbo Qin. Extremal Gromov-Witten invariants of the Hilbert scheme of $3$ Points. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.17

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