Structure theory for some classes of grade three perfect ideals (Q1048206)

The authors study the structure of certain classes of perfect ideals of grade 3. They begin with an analysis of almost complete intersections of grade 3, giving a structure theorem by way of so-called almost complete matrices. They then study the structure of those perfect ideals of grade 3 that are linked to an almost complete intersection by a regular sequence. The structure is described by means of the maps in the minimal free resolution of the ideal. This result generalizes the \textit{D. A. Buchsbaum} - \textit{D. Eisenbud} structure theorem for Gorenstein ideals of grade 3 [Am. J. Math. 99, 447--485 (1977; Zbl 0373.13006)], as well as results of \textit{A. E. Brown} [J. Algebra 105, 308--327 (1987; Zbl 0624.13010)] and \textit{R. Sánchez} [J. Algebra 123, No. 2, 263--288 (1989; Zbl 0679.13001)].