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

2026/07/22 by Abed Abedelfatah
Mathematics · #math.AC

paper · pdf

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.

Related

• The Eisenbud-Green-Harris Conjecture for Defect Two Quadratic Ideals
• A Tight Bound on the Projective Dimension of Four Quadrics
• The Eisenbud-Green-Harris conjecture for fast-growing degree sequences
• The Eisenbud-Green-Harris Conjecture
• An application of liaison theory to the Eisenbud-Green-Harris conjecture