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15 August 2004 Compact moduli of plane curves
Paul Hacking
Duke Math. J. 124(2): 213-257 (15 August 2004). DOI: 10.1215/S0012-7094-04-12421-2

Abstract

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.

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Paul Hacking. "Compact moduli of plane curves." Duke Math. J. 124 (2) 213 - 257, 15 August 2004. https://doi.org/10.1215/S0012-7094-04-12421-2

Information

Published: 15 August 2004
First available in Project Euclid: 5 August 2004

zbMATH: 1060.14034
MathSciNet: MR2078368
Digital Object Identifier: 10.1215/S0012-7094-04-12421-2

Subjects:
Primary: 14H10 , 14J10
Secondary: 14E30

Rights: Copyright © 2004 Duke University Press

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Vol.124 • No. 2 • 15 August 2004
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