Hilbert Coefficients of Quadratic Algebras

Abstract

If R = k[x₁,...,x_n]/I is a graded artinian algebra, then the length of k[x₁,...,x_n]/I^s becomes a polynomial in s of degree n for large s. If we write this polynomial in the form ∑_0<=i<=n (−1)ⁱ e_i (s+n−i−1 choose n−i), then the e_i's are called Hilbert coefficients of I. We will study lengths and Hilbert coefficients of some classes of quadratic algebras.