Depth functions and symbolic depth functions of homogeneous ideals
Huy Tai Ha, Ngo Viet Trung
TL;DR
This paper surveys recent research on the possible numerical behaviors of depth functions associated with powers and symbolic powers of homogeneous ideals in algebraic geometry.
Contribution
It provides a comprehensive overview of recent results and open questions regarding the characterization of depth functions of homogeneous ideals.
Findings
Summarizes known results on depth functions
Identifies open problems in the area
Highlights recent advances in symbolic power analysis
Abstract
We survey recent studies and results on the following problem: which numerical functions can be the depth function of powers and symbolic powers of homogeneous ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Rings, Modules, and Algebras