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Rational Surfaces with Many Nodes

Published online by Cambridge University Press:  04 December 2007

I. Dolgachev ,
M. Mendes Lopes  and
R. Pardini
I. Dolgachev
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109, U.S.A. e-mail: idolga@math.lsa.umich.edu
M. Mendes Lopes
Affiliation:
CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649–003 Lisboa, Portugal. e-mail: mmlopes@lmc.fc.ul.pt
R. Pardini
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2, 56127 Pisa, Italy. e-mail: pardini@dm.unipi.it
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Abstract

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We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \geq b_2-2$ 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.

Keywords

rational surfacenodenodal curvesurface of general type with $p_g=0.$
Type
Research Article
Information
Compositio Mathematica , Volume 132 , Issue 3 , July 2002 , pp. 349 - 363
Copyright
© 2002 Kluwer Academic Publishers