A geographical study of $\overline{\mathcal M}_{2}(\mathbb{P}^2,4)^{\text{main}}$

Abstract

We discuss criteria for a stable map of genus two and degree $4$ to the projective plane to be smoothable, as an application of our modular desingularisation of $\overline{\mathcal M}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$ via logarithmic geometry and Gorenstein singularities.