The Hilbert polynomial of an algebraic curve 
in a projective space of dimension 
is the polynomial 
, for large 
, where 
is the prime ideal defining
and 
is the number of linearly independent forms of degree 
modulo 
.
Hilbert Polynomial
See also
Hilbert Function, Hilbert SeriesExplore with Wolfram|Alpha
References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 36, 1980.Referenced on Wolfram|Alpha
Hilbert PolynomialCite this as:
Weisstein, Eric W. "Hilbert Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HilbertPolynomial.html