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

preprint2014arXivOpen access

We classify log-canonical pairs $(X, Δ)$ of dimension two with $K_X+Δ$ an ample Cartier divisor with $(K_X+Δ)^2=1$ , giving some applications to stable surfaces with $K^2=1$ . A rough classification is also given in the case $Δ=0$ .

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

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Log-canonical pairs and Gorenstein stable surfaces with KX2=1K_X^2=1KX2​=1

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