Monotonicity conjecture for the ellipsoidal superpotential count

For each degree dd, let Tda\mathbf{T}_{d}^{a} denote the count associated with the ellipsoidal superpotential for \CP2\CP^2 with parameter a>1a>1. Monotonicity conjecture. The count TdaR\mathbf{T}_{d}^{a}\in\mathbb{R} is nondecreasing as a function of aR>1a\in\mathbb{R}_{>1}. This conjecture concerns the variation of the holomorphic-curve count with the ellipsoid parameter; the source presents it as a closely related open question, and no resolution is supplied.

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Primary source

Kyler Siegel, “A tree formula for the ellipsoidal superpotential of the complex projective plane”, arXiv:2404.14707 (2024).

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