On the Automorphism Group of a Complex Sphere

Let $X$ be a compact complex threefold with the integral homology of ${\bf S}^6$ and let $Aut(X)$ be its holomorphic automorphism group. By [HKP] and [CDP] the dimension of $Aut(X)$ is at most 2. We prove that $Aut(X)$ cannot be isomorphic to the complex affine group.

1991 Mathematics Subject Classification: 14E05, 32J17, 32M05

Keywords and Phrases: Compact complex threefolds, holomorphic automorphisms, flops

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