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.
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Titolo: | Rigid resolutions and big Betti numbers |
Autori: | |
Data di pubblicazione: | 2004 |
Rivista: | |
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. |
Handle: | http://hdl.handle.net/11567/208228 |
Appare nelle tipologie: | 01.01 - Articolo su rivista |
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