Some cases of the Eisenbud-Green-Harris conjecture

• Autores: Giulio Caviglia, Diane Maclagan
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 427-433
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n3.a3
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• Resumen

  • The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in $\K[x_1,\dots,x_n]$ containing a homogeneous regular sequence $f_1,\dots,f_n$ with $\deg(f_i)=a_i$ has the same Hilbert function as an ideal containing $x_i^{a_i}$ for $1 \leq i \leq n$. In this paper we prove the Eisenbud-Green-Harris conjecture when $a_j > \sum_{i=1}^{j-1} (a_i-1)$ for all $j>1$. This result was independently obtained by the two authors.