Stable pairs descendent rationality conjecture

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Let XX be a nonsingular projective 3-fold, let β∈H2(X,Z)\beta\in H_2(X,\mathbb{Z}), and let

⟨chk1(γ1)⋯chkm(γm)⟩βX,PT\Big\langle \mathsf{ch}_{k_1}(\gamma_1)\cdots \mathsf{ch}_{k_m}(\gamma_m)\Big\rangle_{\beta}^{X,\mathrm{PT}}

be the stable pairs descendent series, where γi∈H∗(X)\gamma_i\in H^*(X) and ki≥0k_i\geq 0. Stable pairs descendent rationality conjecture. The series is the Laurent expansion of a rational function of qq for all such γi\gamma_i and kik_i. Rationality of stable pairs descendent series is a fundamental structural property of the theory; the statement is presented here as a conjecture, with no resolution specified in the source.

References

Primary source

M. Moreira, A. Oblomkov, A. Okounkov and R. Pandharipande, “Virasoro constraints for stable pairs on toric 3-folds”, arXiv:2008.12514 (2020).

Additional references

2 papers in this index state this conjecture (2017–2020). The statement above is taken from the most recent of them; the others are arXiv:1703.01747.

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