Twistors, Kähler manifolds, and bimeromorphic geometry. I

LeBrun, Claude

doi:10.1090/S0894-0347-1992-1137098-5

Twistors, Kähler manifolds, and bimeromorphic geometry. I
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by Claude LeBrun

J. Amer. Math. Soc. 5 (1992), 289-316

DOI: https://doi.org/10.1090/S0894-0347-1992-1137098-5

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Part II: J. Amer. Math. Soc. (1992), 317-325

Abstract:

By considering deformations of the Moishezon twistor spaces of $\mathbb {C}{\mathbb {P}_2}\# \cdot \cdot \cdot \# \mathbb {C}{\mathbb {P}_2}$ constructed in [20], we show that the blow up of ${\mathbb {C}^2}$ at $n$ 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.

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