On Some Twistor Spaces Over 4ℂℙ2

Nobuhiro Honda

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We show that for any positive integer τ there exist on 4ℂℙ2, 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.

Original languageEnglish
Pages (from-to)323-336
Number of pages14
JournalCompositio Mathematica
Volume122
Issue number3
DOIs
Publication statusPublished - 2000 Jul

Keywords

  • Algebraic dimension
  • Elliptic curve
  • Self-dual metric
  • Twistor space

ASJC Scopus subject areas

  • Algebra and Number Theory

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