Constructing infinitely many smooth structures on $3\mathbb{CP}^2 \# n\overline{\mathbb{CP}}^2$

Abstract.

Using Seiberg-Witten theory and rational blow-down procedures of R. Fintushel and R.J. Stern, we construct infinitely many irreducible smooth structures, both symplectic and non-symplectic, on the four-manifold $3\mathbb{CP}^2 \# n \overline{\mathbb{CP}}^2$ for each integer n lying in the interval $10 \leq n \leq 13$.