Projective surfaces with many nodes

Original · EN

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 h¹,¹(X)-1 disjoint (-2)-curves if and only if X is isomorphic to a minimal rational ruled surface F₂ or P² or a fake projective plane. We also describe smooth projective complex surfaces X with h¹,¹(X)-2 disjoint (-2)-curves.