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A complex manifold can be viewed as a smooth manifold. A smooth manifold together with an integrable almost complex structure can be given a complex structure.

Clearly a complex analytic space can be viewed as a real analytic space. My question is now, does there exist a concept on real analytic spaces similar to an almost complex structure on a smooth manifold. And does the "integrability" of such a structure imply that there exists a complex structure on this space such that the associated real analytic space is equal or at least isomorphic to the real analytic space one started with.

Thomas Kurbach
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  • What do you precisely mean for real/complex analytic spaces? – John117 Feb 08 '21 at 16:07
  • I mean a locally ringed space locally isomorphic to $\left(\text{supp}\left(\mathcal{O}{K^n}/ J\right),\mathcal{O}{K^n}/ J\right)$, where $J$ is a coherent ideal sheaf and $K=\mathbb{R},\mathbb{C}$. If it helps you may assume that the real analytic spaces are reduced, i.e. varieties. – Thomas Kurbach Feb 08 '21 at 16:12

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