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Surfaces with many nodes

Igor Dolgachev·Margarida Mendes Lopes·Rita Pardini
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Abstract

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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Igor Dolgachev, Margarida Mendes Lopes, Rita Pardini. 2000-11-14. Surfaces with many nodes. https://arxiv.org/abs/math/0011087

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