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A monomial ideal in a polynomial ring is an ideal generated by monomials.
2
votes
The $k$ th symbolic power of a square free monomial ideal $\rm I$ is $\rm I^{(k)}= \cap_{p\i...
Some references include https://arxiv.org/abs/1309.5082 (see section 3) and Villareal, Monomial Algebras (2nd ed) 2015, Proposition 4.3.24-25.
3
votes
Betti numbers of a Cohen-Macaulay Module in small projective dimension
Yes, using Boij-Söderberg theory. Your Betti table is a convex combination of precisely two pure tables, each determined by Herzog-Kuhl, and the values of $\beta_{1,j}$ let you find the coefficients o …