Compact moduli of plane curves
Algebraic Geometry
2010-03-16 v1
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.
Cite
@article{arxiv.math/0310354,
title = {Compact moduli of plane curves},
author = {Paul Hacking},
journal= {arXiv preprint arXiv:math/0310354},
year = {2010}
}
Comments
46 pages. Final version to be published in Duke Mathematical Journal