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arXiv · 2501.14927

Compact Moduli Spaces of Marked Cubic Plane Curves

Aaron Goodwin
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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.

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Aaron Goodwin. 2025-01-24. Compact Moduli Spaces of Marked Cubic Plane Curves. https://arxiv.org/abs/2501.14927

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