Ideals with Stable Betti Numbers

By Annetta Aramova, Jürgen Herzog, Takayuki Hibi. 2000

82 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ba49118574fc13b35ee00d4c69ca1a481dcf2f1d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Jürgen Herzog
2. Takayuki Hibi
3. Aldo Conca
4. A. Wiebe
5. Annetta Aramova
6. Asia Rauf
7. Adam Van Tuyl
8. Huy Tài Hà

In Computational Theory and Mathematics

1. Jürgen Herzog
2. Takayuki Hibi
3. A. Wiebe
4. Aldo Conca
5. Asia Rauf
6. Huy Tài Hà
7. Susan Morey
8. Adam Van Tuyl

In Geometry and Topology

1. A. Wiebe
2. Jürgen Herzog
3. Takayuki Hibi
4. Aldo Conca
5. Annetta Aramova
6. Huy Tài Hà
7. Susan Morey
8. Ngô Viêt Trung

Citations in the corpus

• Sequentially Cohen-Macaulay modules and local cohomology (2001, background): “c shifted complex of ∆ is the simplicial complex ∆s whose Stanley-Reisner ideal I∆s is generated by the squarefree monomials uσ with u ∈ Gin(I∆). We quote the following properties of I∆s from [1] and [2]: (i) I∆s is a strongly stable ideal in R; (ii) one has the following inequality of graded Betti ”
• Shifting Operations and Graded Betti Numbers (2000, background): “Therefore by [ 4, Theorem 1.1 ], for the graded Betti numbers of I and Gin S .I/ it holds: fliiCj.I/D fliiCj.Gin S .I// for all i and j . On the other”
• Rigid resolutions and big Betti numbers (2003, background): “The following corollary generalizes a result of Aramova, Herzog and Hibi [2], explicitly stated as Theorem 1.2 in [8].”
• The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals (2003, background): “We quote another fact about componentwise linear ideals (see Theorem 1.1 of [ AHH ]):”