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arXiv · 2404.14707

A tree formula for the ellipsoidal superpotential of the complex projective plane

Kyler Siegel
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Abstract

The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as a sum over trees with certain explicit weights. This is a step towards understanding the combinatorial underpinnings of the ellipsoidal superpotential and its mysterious nonvanishing and nondecreasing properties.

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Kyler Siegel. 2024-04-23. A tree formula for the ellipsoidal superpotential of the complex projective plane. https://arxiv.org/abs/2404.14707

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