Stable log surfaces and limits of quartic plane curves (Q1965135)

Let \(C\subseteq\mathbb{P}^2\) be a smooth curve of degree \(d>3\) and look at \((\mathbb{P}^2,C)\) as at a stable log surface. In this paper the author gives a concrete description of the connected moduli scheme of smoothable stable log surfaces when \(d\) is small. In particular the moduli space corresponding to quartic plane curves is shown to coincide with the moduli space of stable curves of genus three.