Depth functions of symbolic powers of homogeneous ideals
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DOI: 10.1007/s00222-019-00897-y
Abstract: This paper addresses the problem of comparing minimal free resolutions of symbolic powers of an ideal. Our investigation is focused on the behavior of the function \({{\,\mathrm{depth}\,}}R/I^{(t)} = \dim R -{{\,\mathrm{pd}\,}}I^{(t)} - 1\), where \(I^{(t)}\)… read more here.
Keywords: mathrm depth; ideal; symbolic powers; mathrm ... See more keywords
ON THE DEPTH OF SYMBOLIC POWERS OF EDGE IDEALS OF GRAPHS
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DOI: 10.1017/nmj.2020.27
Abstract: Abstract Assume that G is a graph with edge ideal $I(G)$ and star packing number $\alpha _2(G)$ . We denote the sth symbolic power of $I(G)$ by $I(G)^{(s)}$ . It is shown that the inequality… read more here.
Keywords: edge ideals; symbolic powers; powers edge; ideals graphs ... See more keywords
Invariants of the symbolic powers of edge ideals
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DOI: 10.1142/s0219498820501844
Abstract: Let [Formula: see text] be a graph and [Formula: see text] be its edge ideal. When [Formula: see text] is the clique sum of two different length odd cycles joined at single vertex then we… read more here.
Keywords: powers edge; invariants symbolic; see text; formula see ... See more keywords