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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 someapplications to stable surfaces with $K^2=1$. A rough classification is alsogiven in the case $\Delta=0$.

Log-canonical pairs and Gorenstein stable surfaces with $K_X^2=1$