Virus infections, Corona surfaces, and extra components in the moduli space of stable surfaces

Abstract

We construct examples of non-smoothable stable surfaces, that we call Corona surfaces, with invariants in a wide range comprising all possible invariants of smooth minimal surfaces of general type but non-standard second plurigenus. We deduce that the moduli space of stable surfaces $\overline{\mathfrak M}_{k,l}$ has least $k-l+2$ connected components distinguished by the second plurigenus and, in particular, it always has more irreducible components than the Gieseker moduli space with the same invariants.