Projective surfaces with many nodes

Abstract

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 ${\mathbf{F}}_2$ 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.

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

References in corpus (2)

• Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups
• The maximum number of singular points on rational homology projective planes