Surfaces with many nodes

Details Surfaces with many nodes Surfaces with many nodes

2000-11-14

arxiv.org/abs/math/0011087v1

Mathematics

Algebraic Geometry

Latex 2e, 17 pages

Scientific paper

We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the second Betti number. In the last section this is applied to the study of minimal complex surfaces of general type with $p_g = 0$ and $K^2 = 8, 9$ which admit an automorphism of order 2.

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