Linkage and sums of ideals

Johnson, Mark

doi:10.1090/S0002-9947-98-01976-X

Linkage and sums of ideals
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by Mark R. Johnson

Trans. Amer. Math. Soc. 350 (1998), 1913-1930

DOI: https://doi.org/10.1090/S0002-9947-98-01976-X

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Abstract:

It is shown (under mild conditions) that the sum of transversal ideals in a regular local ring cannot lie in the linkage class of a complete intersection. For a sum of geometrically linked Cohen-Macaulay ideals, we compute the depths of the conormal module and the first Koszul homology. As applications, we construct general examples of ideals which are strongly Cohen-Macaulay, strongly nonobstructed but not in the linkage class of a complete intersection, and Gorenstein ideals which are strongly nonobstructed but not syzygetic.

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