Mathematical Research Letters

Volume 14, Issue 5, September 2007 pp. 807-823.

Circle and torus actions on equal symplectic blow-ups of $\mathbf{\text{CP}^2}$

Authors: Yael Karshon (1) and Liat Kessler (2)
Author institution: University of Toronto (1) and Massachusetts Institute of Technology (2)

Summary: A manifold obtained by $k$ simultaneous symplectic blow-ups of $\CP^2$ of equal sizes $\epsilon$ (where the size of $\CP^1\subset\CP^2$ is one) admits an effective two dimensional torus action if $k \leq 3$ and admits an effective circle action if $\epsilon < 1/(k-1)$. We show that these bounds are sharp if $\epsilon = 1/n$ where $n$ is a natural number. Our proof combines ``soft" equivariant techniques with ``hard" holomorphic techniques.

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