Poincare' series of monomial rings

Details Poincare' series of monomial rings Poincare' series of monomial rings

2004-12-14

arxiv.org/abs/math/0412282v1

J. Algebra 295 (2006), no. 1, 211-230

Mathematics

Commutative Algebra

15 pages

Scientific paper

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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