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math.AC2017
Hilbert's Syzygy Theorem for monomial ideals
Guillermo Alesandroni
We give a new proof of Hilbert's Syzygy Theorem for monomial ideals. In addition, we prove the following. If S=k[x_1,...,x_n] is a polynomial ring over a field, M is a squarefree m…
math.AC2017
Monomial ideals with large projective dimension
Guillermo Alesandroni
Let S be a polynomial ring in n variables, over an arbitrary field. We give the total, graded, and multigraded Betti numbers of S/M, for every monomial ideal M in S. We also give a…
math.AC2017
Structural decomposition of monomial resolutions
Guillermo Alesandroni
We express the multigraded Betti numbers of an arbitrary monomial ideal in terms of the multigraded Betti numbers of two basic classes of ideals. This decompo- sition has multiple…