Twistors, Kähler manifolds, and bimeromorphic geometry. I

Abstract

By considering deformations of the Moishezon twistor spaces of C P 2 # ⋅ ⋅ ⋅ # C P 2 \mathbb {C}{\mathbb {P}_2}\# \cdot \cdot \cdot \# \mathbb {C}{\mathbb {P}_2} constructed in [20], we show that the blow up of C 2 {\mathbb {C}^2} at n n points in general position admits an asymptotically flat scalar-flat Kähler metric in each Kähler class, at least provided that the given points are nearly collinear.