nLab Chow's theorem

Idea

Chow’s theorem states that a complex analytic space which is given as a closed subset of a complex projective space is a complex algebraic variety.

e.g. (Zhao 13, prop. 5.1, Neeman 07, theorem 1.1.3).

Related concepts

• analytification

• comparison theorem (étale cohomology)

• GAGA

References

Named after:

• Wei-Liang Chow, On compact complex analytic varieties, American Journal of Mathematics 71 4 (1949) 893-914 [doi:10.2307/2372375]

Review:

• Yan Zhao, section 5 of Géométrie algébrique et géométrie analytique, 2013 (pdf)

• Evan Warner, Three approaches to Chow’s theorem (pdf)

• Amnon Neeman, Algebraic and analytic geometry, London Math. Soc. Lec. Note Series 345, 2007 (publisher)