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to have a topology which is regionally such as the subspace topology due to the identification with open subsets of C n displaystyle mathbb C ^ n

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Just one important topic in complex geometry is classification. Because of the rigid nature of complex manifolds and types, the challenge of classifying these spaces is frequently tractable.

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Serre's GAGA theorem asserts that projective complex analytic types are literally algebraic. While this is not strictly genuine for affine varieties, You will find there's class of complex manifolds that act a great deal like affine complex algebraic varieties, identified as Stein manifolds. A manifold X displaystyle X

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