Depth Functions and Symbolic Depth Functions of Homogeneous Ideals

Huy Tài Hà () and Ngo Viet Trung ()
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Huy Tài Hà: Department of Mathematics, Tulane University
Ngo Viet Trung: Vietnam Academy of Science and Technology, International Centre for Research and Postgraduate Training, Institute of Mathematics

A chapter in Commutative Algebra, 2021, pp 429-443 from Springer

Abstract: Abstract We survey recent studies and results on the following problem: for which function f : ℕ → ℤ ≥ 0 $$f: {\mathbb N} \rightarrow {\mathbb Z}_{\ge 0}$$ does there exist a homogeneous ideal Q in a polynomial ring S such that (a) depthS∕Qt = f(t) for all t ≥ 1, or (b) depthS∕Q(t) = f(t) for all t ≥ 1?

Keywords: Depth; Projective dimension; Homogeneous ideal; Monomial ideal; Power; Symbolic power; Bertini-type theorem; Primary 13C15; 13D02; 14B05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/978-3-030-89694-2_13

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