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On the Eisenbud-Green-Harris conjecture


Author: Abed Abedelfatah
Journal: Proc. Amer. Math. Soc. 143 (2015), 105-115
MSC (2010): Primary 13A02; Secondary 13A15
DOI: https://doi.org/10.1090/S0002-9939-2014-12216-7
Published electronically: September 15, 2014
MathSciNet review: 3272735
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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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Abed Abedelfatah
Affiliation: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Email: abed@math.haifa.ac.il

DOI: https://doi.org/10.1090/S0002-9939-2014-12216-7
Keywords: Hilbert function, EGH Conjecture, regular sequence
Received by editor(s): January 16, 2012
Received by editor(s) in revised form: March 28, 2013
Published electronically: September 15, 2014
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.