A Tight Bound on the Projective Dimension of Four Quadrics

Abstract

Motivated by Stillman's question, we show that the projective dimension of an ideal generated by four quadric forms in a polynomial ring is at most 6; moreover, this bound is tight. We achieve this bound, in part, by giving a characterization of the low degree generators of ideals primary to height three primes of multiplicities one and two.

34 pages (to appear in Journal of Pure and Applied Algebra)