• 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...
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  • Thumbnail for Projective variety
    varieties. Hilbert schemes parametrize closed subschemes of P n {\displaystyle \mathbb {P} ^{n}} with prescribed Hilbert polynomial. Hilbert schemes, of which...
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  • Thumbnail for Hilbert's problems
    Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several...
    42 KB (3,697 words) - 17:57, 29 July 2025
  • subscheme is represented by such a point. A simple example of a Hilbert scheme is the Hilbert scheme parameterizing degree d {\displaystyle d} hypersurfaces of...
    28 KB (4,050 words) - 22:20, 30 April 2025
  • {P} ^{n-1}} . Another example is the Hilbert scheme X of a scheme Y, which represents the functor sending a scheme S to the set of closed subschemes of...
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  • In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a...
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  • Thumbnail for Dave Bayer
    Hironaka with a dissertation entitled The Division Algorithm and the Hilbert Scheme. He joined Columbia University thereafter. Bayer is the son of Joan...
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  • not exist as a scheme (Nitsure 2005, p.112). In other words, this gives an example of a smooth complete variety whose Hilbert scheme does not exist....
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  • {\mathcal {O}}_{X}} gives a Hilbert scheme.) For a scheme of finite type X → S {\displaystyle X\to S} over a Noetherian base scheme S {\displaystyle S} , and...
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  • Flat morphism (category Morphisms of schemes)
    universal examples of flat morphisms of schemes are given by Hilbert schemes. This is because Hilbert schemes parameterize universal classes of flat morphisms...
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  • Chow variety (redirect from Chow scheme)
    the term 'Hilbert scheme' is used. Some authors don't subdivide by dimension or degree, others assume the dimension is 0 (i.e. a Hilbert scheme of points)...
    13 KB (2,177 words) - 07:57, 29 April 2025
  • Thumbnail for Robin Hartshorne
    after completing a doctoral dissertation titled Connectedness of the Hilbert scheme under the supervision of John Coleman Moore and Oscar Zariski. He then...
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  • {GL} ({\mathcal {P}}(r),\mathbb {C} )} acts on this Hilbert scheme, and two points in the Hilbert scheme are equivalent if and only if the corresponding polarised...
    53 KB (8,333 words) - 04:19, 17 March 2025
  • reciprocity Hilbert scheme Hilbert space Hilbert dimension Projective Hilbert space Reproducing kernel Hilbert space Rigged Hilbert space Semi-Hilbert space...
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  • because it can be used as the projective space to construct the Hilbert scheme with Hilbert polynomial H C ( t ) {\displaystyle H_{C}(t)} . An irreducible...
    32 KB (4,966 words) - 09:47, 13 June 2025
  • &B\end{matrix}}} In many cases, this universal family is either a Hilbert scheme or Quot scheme, or a quotient of one of them. For example, in the construction...
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  • because SU(2) is isomorphic to Sp(1).) As was shown by Beauville, the Hilbert scheme of k points on a compact hyperkähler 4-manifold is a hyperkähler manifold...
    13 KB (1,682 words) - 19:43, 22 June 2025
  • standard Hilbert scheme theory we can construct a moduli scheme of curves of genus g {\displaystyle g} embedded in some projective space. The Hilbert polynomial...
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  • morphism Semistable elliptic curve Grothendieck's relative point of view Hilbert scheme Grothendieck topology Topos Derived category Descent (category theory)...
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  • Geometric invariant theory (category Scheme theory)
    paper (Hilbert 1893) in classical invariant theory. Geometric invariant theory studies an action of a group G on an algebraic variety (or scheme) X and...
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  • Thumbnail for Alexander Grothendieck
    Tôhoku paper – 1957 mathematics paper by Alexander Grothendieck K-theory Hilbert scheme Homotopy hypothesis Infinitesimal cohomology List of things named after...
    82 KB (8,602 words) - 10:33, 25 July 2025
  • Thumbnail for David Mumford
    Raynaud in 1978. In the second Pathologies paper, Mumford finds that the Hilbert scheme parametrizing space curves of degree 14 and genus 24 has a multiple...
    21 KB (2,134 words) - 16:03, 7 July 2025
  • Thumbnail for Andrei Okounkov
    and the quantum cohomology of the Hilbert scheme of points in the complex plane. Much of his work on Hilbert schemes was joint with Rahul Pandharipande...
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  • symplectic resolutions of quotient singularities, particularly on the Hilbert scheme of n {\displaystyle n} points in the complex plane. They play a fundamental...
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  • systems. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about...
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  • Cataldo & Migliorini (2002) proved the Künneth decomposition for the Hilbert scheme of points in a smooth surface. Conjecture D states that numerical and...
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  • analyzing the locus H g {\displaystyle H_{g}} of stable curves in the Hilbert scheme H i l b P 5 g − 5 − 1 P g ( n ) {\displaystyle \mathrm {Hilb} _{\mathbb...
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  • Hilb may refer to: Emil Hilb (1882–1929), German-Jewish mathematician Hilbert scheme, in algebraic geometry Hilb, Rogal & Hobbs Co. This disambiguation page...
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  • In mathematics, a Severi variety is an algebraic variety in a Hilbert scheme that parametrizes curves in projective space with given degree and geometric...
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  • Quotient by an equivalence relation (category Scheme theory)
    by a Hilbert scheme or disjoint union of Hilbert schemes. In fact, Grothendieck constructed a relative Picard scheme of a flat projective scheme X as...
    2 KB (353 words) - 18:48, 28 November 2023