Rigid resolutions and big Betti numbers

By Aldo Conca, Jürgen Herzog, Takayuki Hibi. 2003

49 citations recorded by the source corpus.

Abstract The Betti-numbers of a graded ideal I in a polynomial ring and the Betti-numbers of its generic initial ideal Gin(I) are compared. In characteristic zero it is shown that if these Betti-numbers coincide in some homological degree, then they coincide in all higher homological degrees. We also compare the Betti-numbers of componentwise linear ideals which are contained in each other and have the same Hilbert polynomial.

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

View Paper: https://www.semanticscholar.org/paper/0146fd265db64109a94ee61cb07cc8ffb746c6a6

Citations in the corpus

• The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals (2003, unknown): “However, for componentwise linear ideals we have (compare Lemma 1.4 of [ CHH ]):”