The lcm-lattice in monomial resolutions
For each monomial ideal \(I\) of a polynomial ring \(S\) (in \(n\) variables over a field \(k)\) which is generated by a sequence of monomials a lattice \({\mathcal L}_I\) is constructed which consists of least common multiples of subsequences of this sequence. It is proved that the lattice \({\mathcal L}_I\) determines the Betti numbers and the minimal free resolution of \(S/I\) and also the algebra structure on \(\text{Tor}^S (S/I,k)\) if additional data in \({\mathcal L}_I\), whose pairs of minimal monomial generators are relatively prime, are known.
scientific article; zbMATH DE number 1489535