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1 results

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

  • Akira Fujiki
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 4 / July 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 1097-1111
    Print publication:
    July 2004
    • Article
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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.