Maulik–Pandharipande's conjecture on Gromov–Witten invariants of blow-ups

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Let XX be a smooth variety, let Z⊂XZ\subset X be a complete intersection of ll divisors W1,…,WlW_1,\ldots,W_l of XX, and let X~\widetilde X be the blow-up of XX along ZZ. Maulik–Pandharipande's conjecture. The descendent absolute Gromov–Witten invariants of X~\widetilde X are determined by the restriction map

H∗(X)→H∗(Z)H^*(X)\rightarrow H^*(Z)

and the descendent absolute Gromov–Witten invariants of XX and ZZ. This conjecture concerns the determination of Gromov–Witten theory under blow-up along a complete intersection; the surrounding discussion states that it has alternative proofs, so it is treated as solved.

References

Primary source

Cheng-Yong Du, “On relative Gromov–Witten invariants of projective completions of vector bundles”, arXiv:1712.04121 (2018).

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