Hilbert coefficients of quadratic algebras

Abstract

If $R=k[x_1,\ldots,x_n]/I$ is a graded artinian algebra, then the length of $k[x_1,\ldots,x_n]/I^s$ becomes a polynomial in $s$ of degree $n$ for large $s$. If we write this polynomial as $\sum_{i=0}^n(-1)^ie_i{s+n-i-1\choose n-i}$, then the $e_i$'s are called Hilbert coefficients of $I$. We will study length and Hilbert coefficients of some classes of quadratic algebras.