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.


  1. 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.
  2. 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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