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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.

2 votes

Strengthening Ax-Grothendieck

A version of OP's claim (with an additional hypothesis) is mentioned in a footnote on the first page of Borel, A. Injective endomorphisms of algebraic varieties. Arch. Math 20, 531–537 (1969). https: …
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