Compact moduli of plane curves

2003/10/22 by Paul Hacking · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Compactification (mathematics) #Degenerate energy levels #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Moduli #Moduli of algebraic curves #Moduli space #Plane curve #Stack (abstract data type) #math.AG #msc:14E30 #msc:14H10 #msc:14J10

paper · pdf · doi:10.1215/s0012-7094-04-12421-2

published as Duke Math. J. 124 (2004), no. 2, 213-257 · 46 pages. Final version to be published in Duke Mathematical Journal

arxiv created 2003/10/22 · openalex publication_date 2004/08/15 · arxiv updated 2010/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We construct a compactification Md of the moduli space of plane curves of degree d. We regard a plane curve C ⊂ℙ2 as a surface-divisor pair (ℙ2,C), and we define Md as a moduli space of pairs (X,D), where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stack Md is smooth and the degenerate surfaces X can be described explicitly.

Citations

• Birational Geometry of Algebraic Varieties
• Semistable divisorial contractions
• Introduction to Toric Varieties. (AM-131)

Cited by

• Wahl singularities in degenerations of del Pezzo surfaces
• Semistable divisorial contractions
• On the quantum periods of del Pezzo surfaces with ⅓ (1, 1) singularities
• Nonexistence of asymptotic GIT compactification