Algebraic and Arithmetic Geometry Seminar

Smoothing of a reducible $I$-surface

by Sönke Rollenske (Philipps-Universität Marburg)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


The moduli space of stable surfaces is a modular compactification of the Gieseker moduli space of (canonical models of) surfaces of general type but has components consisting solely of non-smoothable surfaces. I will construct a smoothing of a particular reducible surface $X$ with $K^2 = 1$ and $p_g = 2$, and thus show that the family of such surfaces is indeed contained in the closure of the smooth locus. $X$ is the union of a singular $K3$ surface and a singular Enriques surface, glued along an elliptic curve.