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2008-05-12T16:23:13Z

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Vipul: New page: ==Definition== Let $R$ be a graded algebra over a field that occurs as a quotient of a multivariate polynomial ring over a field (finitely many variables) by a [[gr...

2008-03-16T21:36:35Z

New page: ==Definition== Let <math>R</math> be a graded algebra over a field that occurs as a quotient of a multivariate polynomial ring over a field (finitely many variables) by a [[gr...

New page

==Definition==

Let <math>R</math> be a [[graded algebra]] over a [[field]] that occurs as a quotient of a [[multivariate polynomial ring over a field]] (finitely many variables) by a [[graded ideal]]. Let <math>M</math> be a finitely generated, graded <math>R</math>-module. The '''Hilbert polynomial''' of <math>M</math>, denoted <math>h_M</math> is a polynomial that takes integers to integers, and such that there exists an integer <math>d_0</math> such that for <math>d \ge d_0</math>, we have:

<math>h_M(d) = dim(M_d)</math>

In other words, the Hilbert polynomial is a polynomial that agrees with the [[Hilbert function]] for sufficiently large values of the variable.

Hilbert polynomial - Revision history

Vipul: 1 revision

Vipul: New page: ==Definition== Let R be a graded algebra over a field that occurs as a quotient of a multivariate polynomial ring over a field (finitely many variables) by a [[gr...

Vipul: New page: ==Definition== Let $R$ be a graded algebra over a field that occurs as a quotient of a multivariate polynomial ring over a field (finitely many variables) by a [[gr...