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I'm taking introductory courses in both Riemann surfaces and algebraic geometry this term. I was surprised to hear that any compact Riemann surface is a projective variety. Apparently deeper links exist.

What is, in basic terms, the relationship between Riemann surfaces and algebraic geometry?

[Tag Riemann-surface does not exist.]

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# Links between Riemann surfaces and algebraic geometry

I'm taking introductory courses in both Riemann surfaces and algebraic geometry this term. I was surprised to hear that any compact Riemann surface is a projective variety. Apparently deeper links exist.

What is, in basic terms, the relationship between Riemann surfaces and algebraic geometry?

[Tag Riemann-surface does not exist.]