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Serre's Condition $R_{k}$ for Sums of Geometric Links
Mark Johnson
,
Bernd Ulrich
Abstract
We investigate what it means that the intersection of a variety with a residual intersection has a low-dimensional singular locus. For schemes having Cohen-Macaulay residual intersections, we prove, for instance, that if the intersection of the scheme with one of its geometric residual intersections has a ‘small’ singular locus, then the scheme can be defined by ‘few’ equations locally.