Resumen de Some cases of the Eisenbud-Green-Harris conjecture

Giulio Caviglia, Diane Maclagan

• 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.