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VOL. 60 | 2010 Projective surfaces with many nodes
JongHae Keum

Editor(s) JongHae Keum, Shigeyuki Kondō, Kazuhiro Konno, Keiji Oguiso

## Abstract

We prove that a smooth projective complex surface $X$, not necessarily minimal, contains $h^{1,1} (X) - 1$ disjoint $(-2)$-curves if and only if $X$ is isomorphic to a relatively minimal ruled rational surface $\mathbf{F}_2$ or $\mathbf{P}^2$ or a fake projective plane.

We also describe smooth projective complex surfaces $X$ with $h^{1,1} (X) - 2$ disjoint $(-2)$-curves.

## Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1214.14031
MathSciNet: MR2761930

Digital Object Identifier: 10.2969/aspm/06010245

Subjects:
Primary: 14J17, 14J26, 14J28, 14J29