About: Hilbert series and Hilbert polynomial

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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 field are three strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra. These notions have been extended to filtered algebras, and graded or filtered modules over these algebras, as well as to coherent sheaves over projective schemes. The typical situations where these notions are used are the following:

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rdfs:label	Hilbert-Funktion (de) Hilbert series and Hilbert polynomial (en) 힐베르트 다항식 (ko) ヒルベルト多項式 (ja) Ряд Гильберта и многочлен Гильберта (ru) Многочлен Гільберта (uk)
rdfs:comment	In der algebraischen Geometrie gibt die Hilbert-Funktion Informationen über die Anzahl der Hyperflächen zu einem gegebenen Grad. Für hinreichend große Argumente stimmt sie mit einem als Hilbert-Polynom bezeichneten Polynom überein. (de) 대수기하학에서 힐베르트 다항식(Hilbert多項式, 영어: Hilbert polynomial)은 대수다양체의 함수 대수의 모양을 담고 있는, 생성함수의 일종이다. (ko) 可換環論における次数環あるいは次数加群のヒルベルト多項式（ヒルベルトたこうしき、英: Hilbert polynomial）は、その（次数環あるいは次数加群の）斉次成分の次元の増加率を測る一変数多項式である。次数付き可換環 S のヒルベルト多項式の次数および最高次係数は、射影代数多様体の次数および次元に関係がある。 (ja) In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra. These notions have been extended to filtered algebras, and graded or filtered modules over these algebras, as well as to coherent sheaves over projective schemes. The typical situations where these notions are used are the following: (en) Функция Гильберта, ряд Гильберта и многочлен Гильберта градуированной коммутативной алгебры, конечно порождённой над полем — это три тесно связанных понятия, которые позволяют измерить рост размерности однородных компонент алгебры. Эти понятия были распространены на и градуированные или фильтрованные модули над этими алгебрами, а также на когерентные пучки над проективными схемами. Эти понятия часто используются в следующих ситуациях: (ru) Функція Гільберта, ряд Гільберта і многочлен Гільберта градуйованої комутативною алгебри і скінченнопородженого градуйованого модуля — три тісно пов'язані поняття, які дозволяють виміряти ріст розмірності однорідних компонент алгебри. Ці поняття були поширені на фільтровані алгебри і градуйовані або фільтровані модулі над цими алгебрами, а також на над проективними схемами. (uk)
dcterms:subject	Commutative algebra Algebraic geometry
Wikipage page ID	6612596 (xsd:integer)
Wikipage revision ID	1070637823 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge Cambridge University Press Binomial coefficient David Hilbert Jordan–Hölder theorem Degree of an algebraic variety General position Free resolution Graded algebra Graded module Monomial ordering Projective scheme Commutative algebra Complete intersection Composition series Computational complexity Computational complexity theory Computer algebra system Zero divisor Ideal (ring theory) Kernel (algebra) Krull dimension Maximal ideal Bézout's theorem Total degree Coherent sheaves Local ring Nilpotent ideal Affine space Algebraic geometry Field (mathematics) Graded vector space Hilbert's syzygy theorem Hilbert–Poincaré series Hilbert–Samuel function Projective variety Regular function Regular ring Gröbner basis Hilbert scheme Irreducible component Commutative algebra Algebraic geometry Advances in Mathematics Coherent sheaf Coherent sheaf cohomology Homogeneous coordinate ring Regular sequence Artinian ring Maple (software) Polynomial ring Springer Science+Business Media Filtered algebra Free module Castelnuovo–Mumford regularity Euler characteristic Quot scheme Multivariate polynomial Exact sequence Proj construction Affine algebraic set Magma (software) Serre twist Graded linear map Formal series Projective algebraic set Numerical polynomial Modules Homogeneous ideal
Link from a Wikipage to an external page	https://www.springer.com/gp/book/9780387977164
sameAs	Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial Hilbert series and Hilbert polynomial
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Citation dbt:Cite_book dbt:Harv dbt:Math dbt:Mvar

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