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

• Autores: Yael Karshon, Liat Kessler
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 5, 2007, págs. 807-823
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n5.a9
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• Resumen

  • 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.