Circle and torus actions on equal symplectic blow-ups of CP2

Yael Karshon, Liat Kessler

Research output: Contribution to journalArticlepeer-review


A manifold obtained by k simultaneous symplectic blow-ups of ℂℙ2 of equal sizes ε (where the size of ℂℙ1 ⊂ ℂℙ2 is one) admits an effective two dimensional torus action if k < 3 and admits an effective circle action if ε < 1/(k - 1). We show that these bounds are sharp if ε = 1/n where n is a natural number. Our proof combines "soft" equivariant techniques with "hard" holomorphic techniques.

Original languageEnglish
Pages (from-to)807-823
Number of pages17
JournalMathematical Research Letters
Issue number5-6
StatePublished - 2007
Externally publishedYes


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