%0 Journal Article %T Log-canonical pairs and Gorenstein stable surfaces with $K_X^2=1$ %A Marco Franciosi %A Rita Pardini %A S£¿nke Rollenske %J Mathematics %D 2014 %I arXiv %R 10.1112/S0010437X14008045 %X We classify log-canonical pairs $(X, \Delta)$ of dimension two with $K_X+\Delta$ an ample Cartier divisor with $(K_X+\Delta)^2=1$, giving some applications to stable surfaces with $K^2=1$. A rough classification is also given in the case $\Delta=0$. %U http://arxiv.org/abs/1403.2159v1