Torus actions on small blow ups of CP^2 - Mathematics > Symplectic GeometryReport as inadecuate




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Abstract: A manifold obtained by k simultaneous symplectic blow-ups of CP^2 of equalsizes epsilon where the size of CP^1 in CP^2 is one admits an effectivetwo-dimensional torus action if k <= 3. We show that it does not admit such anaction if k >=4 and epsilon <= 1-3k 2^{2k}. For the proof, we correspondbetween the geometry of a symplectic toric four-manifold and the combinatoricsof its moment map image. We also use techniques from the theory ofJ-holomorphic curves.



Author: Liat Kessler

Source: https://arxiv.org/







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