Jin–Szenes conjecture for perturbed genus-zero Gromov–Witten invariants

From papers

Let MNkM_N^k be the degree-kk projective Fano hypersurface considered in the paper, and let OhaOhb0(t0,t1,,tN2)\langle {\cal O}_{h^a}{\cal O}_{h^b}\rangle_0(t^0,t^1,\ldots,t^{N-2}) denote the perturbed two-point genus-zero Gromov–Witten invariant. Let w(OhaOhb)0w({\cal O}_{h^a}{\cal O}_{h^b})_0 be the corresponding virtual structure constant, and let xp(t)=xp(t0,t1,,tN2)x^p(t^*)=x^p(t^0,t^1,\ldots,t^{N-2}) be the coordinate transformation specified by the inverse relation referred to in the source. Jin–Szenes conjecture.

OhaOhb0(t0,t1,,tN2)=w(OhaOhb)0(x0(t),x1(t),,xN2(t)).\langle {\cal O}_{h^a}{\cal O}_{h^b}\rangle_0(t^0,t^1,\ldots,t^{N-2})=w({\cal O}_{h^a}{\cal O}_{h^b})_0\bigl(x^0(t^*),x^1(t^*),\ldots,x^{N-2}(t^*)\bigr).

This is the genus-zero Gromov–Witten/virtual-structure-constant correspondence proposed in the cited work. The supplied source does not indicate whether the conjecture has been proved or disproved.

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Sources & referencesView supporting material

Primary source

Masao Jinzenji and Ken Kuwata, “Elliptic Virtual Structure Constants and Generalizations of BCOV-Zinger Formula to Projective Fano Hypersurfaces”, arXiv:2404.07591 (2024).

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