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

  • Nobuhiro Honda (a1)
  • DOI:
  • Published online: 01 July 2000

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.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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