2003/06/16 by Aldo Conca, Conca, Aldo, Juergen Herzog +3 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #msc:13D02
paper · pdf · doi:10.48550/arxiv.math/0306236
arxiv created 2003/06/16 · arxiv updated 2009/11/30
In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let I be a homogeneous ideal in a polynomial ring over a field of characteristic 0. Denote by βi(I) the i-th Betti number of I and by Gin(I) the revlex generic initial ideal of I. In general one has βi(I)≤ βi(Gin(I)) and we show that if βi(I)=βi(Gin(I)) for some i then βj(I)=βj(Gin(I)) for all j>i. In the second part of the paper we answer a question of Eisenbud and Huneke. We prove that if I is m-primary and I⊂ md then βi(md)≤ βi(Gin(I)) for all i.