On the Denominator of the Poincaré series for monomial quotient rings

Abstract

Let $S=\mathbb{k}[x_1,...,x_n]$ be a polynomial ring over a field $\mathbb{k}$ and $I$ a monomial ideal of $S$. It is well known that the Poincaré series of $\mathbb{k}$ over $S/I$ is rational. We describe the coefficients of the denominator of the series and study the multigraded homotopy Lie algebra of $S/I$.

Communications in Algebra, accepted