Gorenstein stable surfaces with $K_X^2=1$ and $\chi ({\mathcal{O}}_X)=2$

Anh Thi Do, Sönke Rollenske

We classify - as far as possible - Gorenstein stable surfaces with $K_X^2=1$ and $\chi ({\mathcal{O}}_X)=2$, describing several strata in the moduli space quite in detail.