Sums of linked ideals

Bernd Ulrich
1990 Transactions of the American Mathematical Society  
It is shown that the sum of two geometrically linked ideals in the linkage class of a complete intersection is again an ideal in the linkage class of a complete intersection. Conversely, every Gorenstein ideal (of height at least two) in the linkage class of a complete intersection can be obtained as a "generalized localization" of a sum of two geometrically linked ideals in the linkage class of a complete intersection. We also investigate sums of doubly linked Gorenstein ideals. As an
more » ... als. As an application, we construct a perfect prime ideal which is strongly non obstructed, but not strongly Cohen-Macaulay, and a perfect prime ideal which is not strongly nonobstructed, but whose entire linkage class is strongly Cohen-Macaulay.
doi:10.1090/s0002-9947-1990-0964902-8 fatcat:w2n2em4xtreefoauq6jmfhuhoy