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 language | English |
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Pages (from-to) | 1897-1920 |
Number of pages | 24 |
Journal | Transactions of the American Mathematical Society |
Volume | 358 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2006 May |
Keywords
- Connected sum
- Elliptic curve
- Moishezon manifold
- Self-dual metric
- Twistor space
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics