English

Compact Moduli Spaces of Marked Cubic Plane Curves

Algebraic Geometry 2026-02-03 v2

Abstract

We study compactifications of the moduli space of a plane cubic curve marked by nn labeled points up to projective equivalence via Geometric Invariant Theory (GIT). Specifically, we provide a complete description of the GIT walls and show that the moduli-theoretic wall-crossing can be understood through analysis of the singularities of the plane curves and the position of the points.

Keywords

Cite

@article{arxiv.2501.14927,
  title  = {Compact Moduli Spaces of Marked Cubic Plane Curves},
  author = {Aaron Goodwin},
  journal= {arXiv preprint arXiv:2501.14927},
  year   = {2026}
}