Computing invariants of semi-log-canonical surfaces (Q2516489)

In this paper the authors study surfaces with semi-log canonical singularities (slc). They first start by giving a method to compute the cohomology and the fundamental group of a variety and the irregularity \(q=h^1(O_X)\). In their main theorem they prove that there are exactly two irregular Gorenstein stable surfaces with \(K^2=1\), and that both surfaces have \(\chi(X)=0\) and \(q(x)=1\). Moreover each one of these surfaces forms a connected component of the moduli space of stable surfaces with \(K^2=1\). \textit{M. Franciosi} et al. [Compos. Math. 151, No. 8, 1529--1542 (2015; Zbl 1331.14037)].