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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.

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Obstruction to the existence of global resolution of coherent sheaf

For the sake of trying to offer some sort of answer based off of Tim's first comment: Let $\mathcal{E}$ be a coherent sheaf on $M$ and $(((E_i, \nabla_i)\to U_i \subset M_i)_{i \in I}$ be a local reso …
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2 votes

Vector bundles over a Stein space are projective

Corollary 2.6.5 in Forstnerič "Stein Manifolds and Holomorphic Mappings". (2nd Edition)
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