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.

Disclaimer: While the language and the pictures in this note are inspired by current events, the actual content is a result of pure mathematics not related to medical research. 9 pages, 11 figures. v2: updated result to distinguish connected components

References in corpus (2)

• Moduli of varieties of general type
• Pluricanonical maps of stable log surfaces