On the moduli space of nodal Enriques surfaces
Enriques surfaces depend on 10 moduli and generically don’t contain smooth rational curves.
Those curves are called “nodal” curves since they have self intersection -2 and can be blown down to an ordinary node. Nodal Enriques surfaces by definition contain at least one nodal curve and these depend on 9 moduli as wa salready known in the 1980s to Cossec and Dolgachev. In a joint work with H. Sterk we found another, more elementary approach starting from double covers of the plane branched in sextic curves invariant under the standard Cremona transformation.
In the talk I’ll explain this in more detail and show how this makes it possible to determine the (infinite!) automorphism group of the generic nodal Enriques surface.