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Twistor spaces of algebraic dimension two associated to a connected sum of projective planes

Published online by Cambridge University Press:  04 December 2007

Akira Fujiki
Akira Fujiki
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, [email protected]
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Abstract

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For any integer $m\geq 4$ we construct twistor spaces of algebraic dimension a = 2 associated to some self-dual structures on mP2, the connected sum of m complex projective planes P2. Together with previously known results this implies that for any $m\geq 5$ all the possible values for algebraic dimension $0\leq a \leq 3$ are attained for some such twistor spaces. Our method is to construct such twistor spaces by small deformations of Joyce twistor spaces.

Keywords

twistor spaceself-dual manifoldalgebraic dimension32J17 (primary)32J2553C15 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 4 , July 2004 , pp. 1097 - 1111
Copyright
Foundation Compositio Mathematica 2004