Powers of ideals generated by Quadratics Sequences

Abstract

Huneke's conjecture that weak d-sequences generate ideals of quadratic type is proved. The proof suggests the definition of quadratic sequences, which are more general than weak d-sequences yet simpler to define and handle, in addition to being just as useful. We extend the theory of d-sequences and weak d-sequences to quadratic sequences. Results of Costa on sequences of linear type are generalized. An example of a two-dimensional local domain in which every system of parameters is a d-sequence in some order but which nevertheless fails to be Buchsbaum is given. A criterion is established for when equality holds in Burch's inequality for an ideal generated by a quadratic sequence.