Stable pairs descendent rationality conjecture

From papers

Let XX be a nonsingular projective 3-fold, let βH2(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 γiH(X)\gamma_i\in H^*(X) and ki0k_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.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

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.

Solutions 0

No solutions have been posted yet.