Compact moduli of plane curves

Abstract

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.

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

References in corpus (1)

• Semistable divisorial contractions

Cited by in corpus (18)

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• Semistable divisorial contractions
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• Full exceptional collections for anticanonical log del Pezzo surfaces