Hilbert Scheme
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High Quality Content by WIKIPEDIA articles! 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 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 (Alexander Grothendieck 1961). The Hilbert scheme HilbPn of n-dimensional projective space classifies closed subschemes of projective space in the following sense: For any locally Noetherian scheme S, the set of S-valued points Hom(S,HilbPn) of the Hilbert scheme is naturally isomorphic to the set of closed subschemes of Pn×S that are flat over S. The closed subschemes of Pn×S that are flat over S can informally be thought of as the families of subschemes of projective space parameterized by S.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131199882
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131199882
- Format Fachbuch
- Titel Hilbert Scheme
- Herausgeber Betascript Publishing
- Anzahl Seiten 88
- Genre Mathematik
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