Boij-Soderberg theory for ideals generated by degree 2

Abstract

In Boij-Soderberg theory, it is known that for any degree sequence $\mathbf{d}$, there exists a finitely generated module that has a pure resolution of type $\mathbf{d}$. On the other hand, in the case of ideal, there are two necessary conditions for the degree sequence, which $\mathbf{d}$ satisfies them if there is an ideal that has a pure resolution of type $\mathbf{d}$. In this paper, by theory of generic initial ideals and Boij-Soderberg decompositions, we construct the degree sequence which satisfies these conditions but there is no such an ideal.

arXiv comment14 pages, Main result has already been known

References in corpus (1)

• Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture