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Log-canonical pairs and Gorenstein stable surfaces with
$K_{X}^{2}=1$
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 8 / August 2015
- Published online by Cambridge University Press:
- 15 April 2015, pp. 1529-1542
- Print publication:
- August 2015
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- Article
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We classify log-canonical pairs
$(X,{\rm\Delta})$ of dimension two such that 
$K_{X}+{\rm\Delta}$ is an ample Cartier divisor with 
$(K_{X}+{\rm\Delta})^{2}=1$, giving some applications to stable surfaces with 
$K^{2}=1$. A rough classification is also given in the case where 
${\rm\Delta}=0$.
