Projective surfaces with many nodes

Details Projective surfaces with many nodes Projective surfaces with many nodes

2009-08-30

arxiv.org/abs/0908.4372v2

Mathematics

Algebraic Geometry

9 pages. A missing case was added to Theorem 1.4. Minor changes were made

Scientific paper

The paper is a generalization of a result of I. Dolgachev, M. Mendes Lopes, and R. Pardini. 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 minimal rational ruled surface ${\bf F}_2$ or ${\bf P}^2$ or a fake projective plane. We also describe smooth projective complex surfaces $X$ with $h^{1,1}(X)-2$ disjoint $(-2)$-curves.

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