# Blowing down

In mathematics, **blowing down** is a type of geometric modification in algebraic geometry.^{[1]} It is the inverse operation of blowing up.^{[2]}

On an algebraic surface, blowing down a curve lying on the surface is a typical effect of a birational transformation. The curves that blow down, to a non-singular point, are of a special kind: they are rational curves, with self-intersection number −1.

## References

- ↑ Andradas, Carlos; Ruiz, Jesús M. (1995),
*Algebraic and Analytic Geometry of Fans*, Memoirs of the American Mathematical Society,**553**, American Mathematical Society, p. 108, ISBN 9780821862766. - ↑ Dieudonné, Jean (1982),
*A panorama of pure mathematics, as seen by N. Bourbaki*, Pure and Applied Mathematics,**97**, Academic Press, p. 105, ISBN 9780080874135.

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