A tree formula for the ellipsoidal superpotential of the complex projective plane
Symplectic Geometry
2024-04-24 v1
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.
Keywords
Cite
@article{arxiv.2404.14707,
title = {A tree formula for the ellipsoidal superpotential of the complex projective plane},
author = {Kyler Siegel},
journal= {arXiv preprint arXiv:2404.14707},
year = {2024}
}