English

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}
}