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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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Proving algebraicity of compact Riemann surfaces without Chow's theorem

I am trying to write a report for a complex analysis class where I prove Riemann-Roch and apply it to prove algebraicity of compact Riemann surfaces. While writing this, I found that Riemann-Roch quit …
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