On the projective dimension of 5 quadric almost complete intersections with low multiplicities

Abstract

Let S be a polynomial ring over an alge-braically closed field k and p = (x; y; z;w) a homogeneous height 4 prime ideal. We give a finite characterization of the degree 2 component of ideals primary to p, with multiplicity e ≤ 3. We use this result to give a tight bound on the projective dimension of almost complete intersections generated by five quadrics with e ≤ 3. © 2019 Rocky Mountain Mathematics Consortium.