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Log-canonical pairs and Gorenstein stable surfaces with $K_{X}^{2}=1$

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  15 April 2015

Marco Franciosi ,
Rita Pardini  and
Sönke Rollenske
Marco Franciosi
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, I-56127 Pisa, Italy email franciosi@dm.unipi.it
Rita Pardini
Affiliation:
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, I-56127 Pisa, Italy email pardini@dm.unipi.it
Sönke Rollenske
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany email rollenske@math.uni-bielefeld.de
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Abstract

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 ${\rm\Delta}=0$.

Keywords

log-canonical pairstable surfacegeography of surfaces

MSC classification

Primary: 14J10: Families, moduli, classification 14J29: Surfaces of general type
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 8 , August 2015 , pp. 1529 - 1542
Copyright
© The Authors 2015 

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