Nikola Kuzmanovski

University of Notre Dame

Some results on the Eisenbud-Green-Harris and the weak Lefschetz property

We will present some results on the Eisenbud-Green-Harris (EGH) conjecture that cover historically difficult cases of like the case when the degree of the regular sequence are all the same. These cases in any number of variables and exclude only a finite number of degrees for the regular sequence. We will connect the weak Lefschetz property (WLP) to the EGH conjecture, and prove that a complete intersection plus an ideal generated by general linear forms satisfies the WLP in a limited range.