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INTRODUCTION to HILBERT SCHEMES EXERCISES Hilbert Form
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People also ask
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What is the Hilbert scheme introduction?
The Hilbert scheme HilbP (Pn) is a parameter space whose closed points correspond to subschemes of Pn with Hilbert polynomial P. The topology on HilbP (Pn) gives a notion of when two subschemes are “close”. Many other moduli spaces are constructed by realizing them as subschemes of the Hilbert scheme.
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What is the Hilbert scheme of projective space?
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.
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What is the Hilbert scheme Grothendieck?
The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by Alexander Grothendieck (1961). Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
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What is the history of scheme theory?
Scheme theory was introduced by Alexander Grothendieck in 1960 in his treatise Éléments de géométrie algébrique (EGA); one of its aims was developing the formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne).
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