Family Seiberg-Witten equation on Kahler surface and $π_i(\Symp)$ on multiple-point blow ups of Calabi-Yau surfaces

Let $ω$ be a Kahler form on $M$, which is a torus $T^4$, a $K3$ surface or an Enriques surface, let $M\#n\overline{\mathbb{CP}^2}$ be $n-$point Kahler blowup of $M$. Suppose that $κ=[ω]$ satisfies certain irrationality condition. Applying techniques related to deformation of complex objects, we exte