 Symplectic blowup

A symplectic blowup at a point removes a small symplectic ball and collapses its Hopf-circle boundary fibers, replacing the center by an exceptional divisor $E\cong {\mathbb{CP}}^{n-1}$. The resulting form agrees with the original form away from the surgery region, and its integral over a projective line in $E$ records the blowup size. In real dimension four, $E\cong {\mathbb{CP}}^1$ and $E^2=-1$.