Duke Mathematical Journal

Compact moduli of plane curves

Paul Hacking

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We construct a compactification $\mathcal{M}$d 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 $\mathcal{M}$d 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 $\mathcal{M}$d is smooth and the degenerate surfaces X can be described explicitly.

Article information

Duke Math. J. Volume 124, Number 2 (2004), 213-257.

First available: 5 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic) 14J10: Families, moduli, classification: algebraic theory
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)


Hacking, Paul. Compact moduli of plane curves. Duke Mathematical Journal 124 (2004), no. 2, 213--257. doi:10.1215/S0012-7094-04-12421-2. http://projecteuclid.org/euclid.dmj/1091735975.

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