Compact Moduli Spaces of Marked Cubic Plane Curves
Aaron Goodwin

TL;DR
This paper explores the GIT-based compactifications of the moduli space of marked cubic plane curves, analyzing wall-crossings through curve singularities and point configurations.
Contribution
It provides a complete description of GIT walls and links moduli space wall-crossing to singularities and point positions on cubic curves.
Findings
Complete GIT wall description for marked cubic plane curves
Connection between wall-crossing and curve singularities
Analysis of point configurations affecting moduli space stability
Abstract
We study compactifications of the moduli space of a plane cubic curve marked by \(n\) 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Mathematical Approximation and Integration
