Journal of Symplectic Geometry

Volume 15 (2017)

Number 4

Distinguishing symplectic blowups of the complex projective plane

Pages: 1089 – 1128



Yael Karshon (Department of Mathematics, University of Toronto, Ontario, Canada)

Liat Kessler (Department of Mathematics, Physics, and Computer Science, University of Haifa at Oranim, Tivon, Israel)


A symplectic manifold that is obtained from $\mathbb{CP}^2$ by $k$ blowups is encoded by $k + 1$ parameters: the size of the initial $\mathbb{CP}^2$, and the sizes of the blowups. We determine which values of these parameters yield symplectomorphic manifolds.

Received 20 July 2015

Accepted 6 March 2016

Published 28 November 2017