Modular compactifications of ℳ2,n with Gorenstein curves

We study the geometry of Gorenstein curve singularities genus two, and their stable limits. These come in two families, corresponding to either Weierstrass or conjugate points on a semistable tail. For every $1\leq m <n$, stability condition - using one markings as reference point, therefore not $\mathfrak S_n$-symmetric defines proper Deligne-Mumford stacks $\overline{\mathcal M}_{2,n}^{(m)}$ containing locus smooth curves dense open substack.