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Blow-Up Center

A blow-up center is the closed subscheme Z of a scheme X along which an algebraic blow-up b:Bl_(Z)(X)->X is performed. Equivalently, the center is specified by an ideal sheaf that is a quasi-coherent sheaf and defines Z (Stacks Project 2026).

The morphism b is an isomorphism away from its center, and the inverse image of the center is the exceptional divisor.

See also

Algebraic Blow-Up, Exceptional Divisor, Ideal Sheaf, Quasi-Coherent Sheaf, Subscheme

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References

Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.The Stacks Project Authors. "Blowing Up." §31.33 in The Stacks Project, Tag 01OF, 2026. https://stacks.math.columbia.edu/tag/01OF.

Cite this as:

Weisstein, Eric W. "Blow-Up Center." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Blow-UpCenter.html

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