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
Classification
Statement FormCharacterization Theorem 1 StatementAny analytic subvariety in projective space is actually algebraic. 1 Connections
Sources
1. Chow's theorem (Wikipedia)
Introduction, first listed theoremQuote, Introduction, first listed theorem
Any analytic subvariety in projective space is actually algebraic
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