Quadratic Ideals in Six Variables and the Eisenbud--Green--Harris Conjecture

Abstract

In this paper, we study the Eisenbud--Green--Harris (EGH) conjecture for ideals generated by quadrics. We establish a sharp lower bound for the dimension of the cubic component of an ideal generated by a regular sequence of six quadrics and two additional quadrics in six variables. Furthermore, we prove the Eisenbud--Green--Harris conjecture for almost complete intersections of quadrics in six variables.

arXiv comment7 pages