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

Marco Franciosi; Rita Pardini; Sönke Rollenske

doi:10.1112/S0010437X14008045

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

Algebraic Geometry 2015-08-19 v1

Authors: Marco Franciosi , Rita Pardini , Sönke Rollenske

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Abstract

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 $\Delta=0$ .

Keywords

log-canonical pairs Gorenstein stable surfaces ample Cartier divisor classification stable surfaces $K^2=1$

Cite

@article{arxiv.1403.2159,
  title  = {Log-canonical pairs and Gorenstein stable surfaces with $K_X^2=1$},
  author = {Marco Franciosi and Rita Pardini and Sönke Rollenske},
  journal= {arXiv preprint arXiv:1403.2159},
  year   = {2015}
}

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