Commentarii Mathematici Helvetici

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Volume 79, Issue 4, 2004, pp. 826–839
DOI: 10.1007/s00014-004-0812-2

Published online: 2004-12-31

Rigid resolutions and big Betti numbers

Aldo Conca[1], Jürgen Herzog[2] and Takayuki Hibi[3]

(1) Università di Genova, Italy
(2) Universität GHS Essen, Germany
(3) Graduate School of Science, Osaka University, Japan

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.

Keywords: free resolutions, generic initial ideals, componentwise linear ideals

Conca Aldo, Herzog Jürgen, Hibi Takayuki: Rigid resolutions and big Betti numbers. Comment. Math. Helv. 79 (2004), 826-839. doi: 10.1007/s00014-004-0812-2