Computing invariants of semi-log-canonical surfaces
  We describe some methods to compute fundamental groups, (co)homology, and irregularity of semi-log-canonical surfaces.   As an application, we show that there are exactly two irregular Gorenstein stable surfaces with $K^2=1$, both of which have $\chi(X) = 0$ and $\mathrm{Pic}^0(X)=\mathbb{C}^*$ but different homotopy type. 
Marco Franciosi, Rita Pardini, S\"onke Rollenske
math.AG