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Poincare' series of monomial rings

Alexander Berglund
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Abstract

Let R be the quotient of a polynomial ring over a field k by an ideal generated by monomials. We derive a formula for the multigraded Poincare' series of R, i.e., the generating function for the ranks of the modules in a minimal multigraded free resolution of k over R. The formula can be expressed in terms of the homology of lower intervals in a certain lattice associated to the minimal set of generators for the ideal.

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Alexander Berglund. 2004-12-14. Poincare' series of monomial rings. https://arxiv.org/abs/math/0412282

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