Sums of linked ideals

Ulrich, Bernd

doi:10.1090/S0002-9947-1990-0964902-8

Sums of linked ideals
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Trans. Amer. Math. Soc. 318 (1990), 1-42 Request permission

Abstract:

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 application, we construct a perfect prime ideal which is strongly nonobstructed, but not strongly Cohen-Macaulay, and a perfect prime ideal which is not strongly nonobstructed, but whose entire linkage class is strongly Cohen-Macaulay.

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