2005/08/17 by Benjamin Richert, Benjamin P. Richert, Richert, Benjamin P. +2
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #msc:13D02 #msc:13D40 #msc:13F20
paper · pdf · doi:10.48550/arxiv.math/0508334
32 pages
arxiv created 2005/08/17 · arxiv updated 2009/12/01
The n-type vectors introduced by Geramita, Harima and Shin are in 1-1 correspondence with the Hilbert functions Artinian of lex ideals. Letting \mathbbA =\a1,..., an\ define the degrees of a regular sequence, we construct \rm lpp_≤\mathbbA-vectors which are in 1-1 correspondence with the Hilbert functions of certain lex plus powers ideals (depending on \mathbbA). This construction enables us to show that the residual of a lex plus powers ideal in an appropriate regular sequence is again a lex plus powers ideal. We then use this result to show that the Eisenbud-Green-Harris conjecture is equivalent to showing that lex plus powers ideals have the largest last graded Betti numbers (it is well-known that the Eisenbud-Green-Harris conjecture is equivalent to showing that lex plus powers ideals have the largest first graded Betti numbers).