Hilbert scheme

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In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some fixed scheme. In fact such a parameter space breaks up into pieces, each piece corresponding to a Hilbert polynomial. The basic theory of Hilbert schemes was developed by Alexander Grothendieck around 1960.

[edit] References

  • David Mumford, Lectures on Curves on an Algebraic Surface
  • A. Grothendieck, Les Schémas de Hilbert, Séminaire Bourbaki, t. 13, 1960/61, no. 221.
  • Fundamental Algebraic Geometry: Grothendieck's FGA Explained (OUP 2006)
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