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.
Cite this article
Jürgen Herzog, Aldo Conca, Takayuki Hibi, Rigid resolutions and big Betti numbers. Comment. Math. Helv. 79 (2004), no. 4, pp. 826–839