Depth and regularity of powers of sums of ideals
By Huy Tài Hà, Ngô Viêt Trung, Tran Nam Trung. 2015
74 citations recorded by the source corpus.
Given arbitrary homogeneous ideals I and J in polynomial rings A and B over a field k, we investigate the depth and the Castelnuovo–Mumford regularity of powers of the sum $$I+J$$I+J in $$A \otimes _k B$$A⊗kB in terms of those of I and J. Our results can be used to study the behavior of the depth and regularity functions of powers of an ideal. For instance, we show that such a depth function can take as its values any infinite non-increasing sequence of non-negative integers.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d7a23dfc34a998d8d3bc94c7a3fb43938f7c5862
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Powers of sums and their homological invariants (2016, methodology): “Note that in [25], the notation lin(I) was used in place of rstab(I).”
- Symbolic powers of cover ideal of very well-covered and bipartite graphs (2016, unknown): “ the same for every very well-covered graphs. Computing and finding bounds for the regularity of powers of a monomial ideal have been studied by a number of researchers (see for example [2], [3], [5], [14]). It is well-known that reg(Is) is asymptotically a linear function for s ≫ 0. However, it is u”