Hilbert scheme

In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by (AlexanderGrothendieck 1961). Hironaka's example shows that non-projective varieties need not have Hilbert schemes.

单词	Hilbert scheme
释义	Hilbert scheme 英语百科 Hilbert scheme In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by (AlexanderGrothendieck 1961). Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
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