Theorem

Chow's Theorem

Geometry

Chow's Theorem states that every closed analytic subvariety of complex projective space is in fact an algebraic variety, meaning it can be described as the common zero set of a finite collection of homogeneous polynomials rather than merely by analytic equations. Named for Wei-Liang Chow, it is a foundational result linking complex analytic geometry to algebraic geometry, showing that the analytic and algebraic categories coincide for subvarieties of projective space even though the two categories differ substantially in more general settings.

Facts

Statement

Any analytic subvariety in projective space is actually algebraic. 1

Proof Year

1949 2

Classification

Statement Form

Characterization Theorem 1

Connections

Source Chow's theorem (Wikipedia)

Sources

1. Chow's theorem (Wikipedia)

Introduction, first listed theorem
Any analytic subvariety in projective space is actually algebraic
Proved By: Wei-Liang Chow, Lead
In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow: Chow's theorem: Any analytic subvariety in projective space is actually algebraic.

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2. MacTutor History of Mathematics, University of St Andrews: Wei-Liang Chow - MacTutor History of Mathematics

MacTutor History of Mathematics, University of St AndrewsBiography

Quote, Biography

Chow's theorem that a compact analytic variety in a projective space is algebraic was published in 1949

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Chow's Theorem

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