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Incoming links: Normalization of an algebraic variety
Normalization of an algebraic curve Created 2026-09-24 Updated 2026-10-13
This is the one-dimensional case of normalization of an algebraic variety, constructed from integral closures of coordinate rings.
The normalization of an irreducible algebraic curve is a normal, hence regular, curve with a finite birational morphism to the original curve. Over a perfect field this regular curve is smooth.