Compact moduli of plane curves

Original · EN

We construct a compactification Md of the moduli space of plane curves of degree d. We regard a plane curve C as a surface-divisor pair (P²,C) and define Md 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 Md is smooth and the degenerate surfaces X can be described explicitly.