Candidates for nonzero Betti numbers of monomial ideals |
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Authors: | Ali Akbar Yazdan Pour |
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Affiliation: | 1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iranyazdan@iasbs.ac.ir |
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Abstract: | Let I be a monomial ideal in the polynomial ring S generated by elements of degree at most d. In this paper, it is shown that, if the i-th syzygy of I has no elements of degrees j,…,j+(d?1) (where j≥i+d), then (i+1)-th syzygy of I does not have any element of degree j+d. Then we give several applications of this result, including an alternative proof for Green–Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fröberg’s theorem on classification of square-free monomial ideals generated in degree 2 with linear resolution. Among all, we deduce a partial result on subadditivity of the syzygies for monomial ideals. |
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Keywords: | Betti numbers Fröberg’s theorem Green–Lazarsfel index syzygy |
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