边理想不变链的渐近深度

arXiv - MATH - Commutative Algebra Pub Date : 2024-09-10 DOI:arxiv-2409.06252

Tran Quang Hoa, Do Trong Hoang, Dinh Van Le, Hop D. Nguyen, Thai Thanh Nguyen

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引用次数: 0

摘要

我们完全确定了边理想链的渐近深度，也就是在正整数上递增函数的单项式 Inc 的作用下不变的渐近投影维数。我们的结果及其证明还揭示了相应图及其独立复数令人惊讶的组合和拓扑性质。特别是，我们能够确定这些独立复数的所有还原同调群的渐近行为。

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Asymptotic depth of invariant chains of edge ideals

We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes.

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arXiv - MATH - Commutative Algebra

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