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Suppose we are given two integer numbers $p$ and $q$ such that $p+q\equiv 0 \pmod{12}$. There is a result saying that for every such pair there exists a non necessarily connected almost complex manifold of dimension $4$ such that its Chern numbers are equal to $p$ and $q$. Could you give me a reference for the proof of this result?

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A. Van de Ven: On the Chern numbers of certain complex and almost complex manifolds, Proc. Natl. Acad. Sci. USA 55, 1624-1627 (1966). ZBL0144.21003.

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