Non-moishezon twistor spaces of 4CP2 with non-trivial automorphism group

Nobuhiro Honda

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1 Citation (Scopus)

Abstract

We show that a twistor space of a self-dual metric on 4CP2 with U(1)-isometry is not Moishezon iff there is a C*-orbit biholomorphic to a smooth elliptic curve, where the C*-action is the complexification of the U(1)-action on the twistor space. It follows that the U(1)-isometry has a two-sphere whose isotropy group is Z2. We also prove the existence of such twistor spaces in a strong form to show that a problem of Campana and Kreußler is affirmative even though a twistor space is required to have a non-trivial automorphism group.

Original languageEnglish
Pages (from-to)1897-1920
Number of pages24
JournalTransactions of the American Mathematical Society
Volume358
Issue number5
DOIs
Publication statusPublished - 2006 May

Keywords

  • Connected sum
  • Elliptic curve
  • Moishezon manifold
  • Self-dual metric
  • Twistor space

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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