On the Eisenbud-Green-Harris conjecture

Abedelfatah, Abed

doi:10.1090/S0002-9939-2014-12216-7

On the Eisenbud-Green-Harris conjecture
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Proc. Amer. Math. Soc. 143 (2015), 105-115 Request permission

Abstract:

It has been conjectured by Eisenbud, Green and Harris that if $I$ is a homogeneous ideal in $k[x_1,\dots ,x_n]$ containing a regular sequence $f_1,\dots ,f_n$ of degrees $\deg (f_i)=a_i$, where $2\leq a_1\leq \cdots \leq a_n$, then there is a homogeneous ideal $J$ containing $x_1^{a_1},\dots ,x_n^{a_n}$ with the same Hilbert function. In this paper we prove the Eisenbud-Green-Harris Conjecture when $f_i$ splits into linear factors for all $i$.

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