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The residuals of lex plus powers ideals and the Eisenbud-Green-Harris conjecture | | Benjamin P. Richert
; Sindi Sabourin
; | | Date: |
17 Aug 2005 | | Subject: | Commutative Algebra MSC-class: 13F20 (Primary) 13D02, 13D40 (Secondary) | math.AC | | Abstract: | The $n$-type vectors introduced by Geramita, Harima and Shin are in 1-1 correspondence with the Hilbert functions Artinian of lex ideals. Letting $mathbb{A} ={a_1,..., a_n}$ define the degrees of a regular sequence, we construct ${
m lpp}_{lemathbb{A}}$-vectors which are in 1-1 correspondence with the Hilbert functions of certain lex plus powers ideals (depending on $mathbb{A}$). 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). | | Source: | arXiv, math.AC/0508334 | | Services: | Forum | Review | PDF | Favorites | |
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