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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…

Hilbert schemes and hyperkähler geometry, Hilbert scheme of projective space & Overview

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Overview

Hilbert scheme of projective space

Functorial interpretation

Examples of Hilbert schemes

Hilbert scheme of points on a manifold

Hilbert schemes and hyperkähler geometry

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Hilbert scheme

Nodes49
Edges48
Triples167
Avg. degree1.96
Density0.040816
Components1

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Hilbert scheme

Top relations

related to References · 88
Hilbert scheme → Adrien Douady, Alain Guichardet, Alexander, Algebraic, Algebraic Surface, American Journal, American Mathematical Society, Angelo, Annals, Arnaud, Barbara, Beauville, Berlin, BFb0073491, Bibcode, Chern, Connectedness, Construction, CS1, Curves
related to Hilbert schemes and hyperkähler geometry · 18
Hilbert scheme → Akira Fujiki, Arnaud Beauville, Calabi, Hartogs, Hence, Hilbert, Indeed, It, K3, Kodaira, Kummer, Kähler, Let, Singularities, Sym, The, This, Yau
related to External links · 14
Hilbert scheme → Aaron, Barbara, Bertram, Construction, CS1, Diane, Hilbert, Hilbert Schemes, Ivan, Losev, Maclagan, Notes, PDF, URL
related to Hilbert scheme of projective space · 9
Hilbert scheme → Each, For, Hilb, Hilbert, Noetherian, S-valued, Spec, The, The Hilbert
related to Construction as a determinantal variety · 8
Hilbert scheme → For, Grassmannian, Grothendieck, Hilb, Hilbert, If, Its, Using
related to Fano schemes of hypersurfaces · 6
Hilbert scheme → Fano, For, Given, Hilbert, One, This
related to Hilbert scheme of points · 5
Hilbert scheme → Another, Delta, For, Hilbert, Riemann
related to Hilbert scheme of points on a manifold · 5
Hilbert scheme → Chow, Fogarty, Hilbert, Informally, There
related to Degree d hypersurfaces · 4
Hilbert scheme → For, Gamma, Hilbert, The Hilbert
related to Functorial interpretation · 4
Hilbert scheme → For, Hilbert, Sch/S, There

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Important terminology

hilbert displaystyle scheme mathbb space points schemes projective subschemes algebraic flat times dimension surface mr polynomial given smooth isbn curves

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hilbert schemeis ascheme that is the parameter space for the closed subschemes of some projective space0.90text
Hilbert schemeis adisjoint union of projective subschemes corresponding to Hilbert polynomials0.90text
Hilbert schemerelated to Construction as a determinantal varietyGrothendieck0.60section
Hilbert schemerelated to Construction as a determinantal varietyHilbert0.60section
Hilbert schemerelated to Construction as a determinantal varietyHilb0.60section
Hilbert schemerelated to Construction as a determinantal varietyGrassmannian0.60section
Hilbert schemerelated to Construction as a determinantal varietyIts0.60section
Hilbert schemerelated to Construction as a determinantal varietyIf0.60section
Hilbert schemerelated to Construction as a determinantal varietyFor0.60section
Hilbert schemerelated to Construction as a determinantal varietyUsing0.60section
Hilbert schemerelated to Degree d hypersurfacesThe Hilbert0.60section
Hilbert schemerelated to Degree d hypersurfacesGamma0.60section

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