Hilbert polynomial
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In mathematics, the Hilbert polynomial of a graded commutative algebra
- A = ⊕An
over a field k that is generated by the finite dimensional space A1 is the unique polynomial f(x) with rational coefficients such that
- f(n) = dimk An
for all but finitely many positive integers n. In other words, Hilbert polynomial refers to the Hilbert function, in those cases where almost all the function's values are given by a polynomial.
The Hilbert polynomial of a finitely generated graded module over A is defined similarly.
The Hilbert polynomial of a projective variety V in Pn is defined as the Hilbert polynomial of the projective coordinate ring of V.
