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On Some Twistor Spaces Over $4{\Bbb CP}$2

Published online by Cambridge University Press:  04 December 2007

Nobuhiro Honda
Nobuhiro Honda
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, 739-8526, Japan. E-mail: honda@math.sci.hiroshima-u.ac.jp
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Abstract

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We show that for any positive integer τ there exist on $4{\Bbb CP}$2, the connected sum of four complex projective planes, twistor spaces whose algebraic dimensions are two. Here, τ appears as the order of the normal bundle of C in S, where S is a real smooth half-anti-canonical divisor on the twistor space and C is a real smooth anti-canonical divisor on S. This completely answers the problem posed by Campana and Kreussler. Our proof is based on the method developed by Honda, which can be regarded as a generalization of the theory of Donaldson and Friedman.

Keywords

twistor spaceself-dual metricalgebraic dimensionelliptic curve

Information

Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 3 , July 2000 , pp. 323 - 336
Copyright
© 2000 Kluwer Academic Publishers