Compact moduli of plane curves

Details Compact moduli of plane curves Compact moduli of plane curves

2003-10-22

arxiv.org/abs/math/0310354v1

Duke Math. J. 124 (2004), no. 2, 213-257

Mathematics

Algebraic Geometry

46 pages. Final version to be published in Duke Mathematical Journal

Scientific paper

10.1215/S0012-7094-04-12421-2

We construct a compactification M_d of the moduli space of plane curves of
degree d. We regard a plane curve C as a surface-divisor pair (P^2,C) and
define 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 M_d is smooth and
the degenerate surfaces X can be described explicitly.

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