ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 13, 14 Ko, Hyoung J., Yonsei University, Seoul 120-749, Korea Some complete intersection and their minimal prime ideals As a consequence of the Buchsbaum-Eisenbud structure theorem, the Gorenstein ideals of grade three have an odd number generators. In fact, the ideals ℑ in a regular local ring R such that R/ℑ is Gorenstein are subject to some surprising restrictions: If gradeℑ = g, then ℑ may be minimally generated by g elements but not by g + 1 elements. If g ≥ 4, every minimal number of generators ≥ g + 2 is possible. A certain class of complete intersection Gorenstein ideals of grade g will be presented. In particular, we characterize the complete intersections of grade three by means of minimal prime ideals and linkage theory. Reference: D. A. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions and some structure theorems for ideals for codimension 3, Amer. J. Math. 99 (1977), 447–485.