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Serre’s Condition R k for Sums of Geometric Links

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA

    Mark Johnson

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Bernd Ulrich

Authors
  1. Mark Johnson
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  2. Bernd Ulrich
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Corresponding author

Correspondence to Bernd Ulrich.

Additional information

Dedicated to Ngô Việt Trung for his numerous contributions to commutative algebra and his tireless work on behalf of mathematics in the developing world

The first author thanks the Department of Mathematics of Purdue University for its hospitality. The second author was supported in part by the NSF

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Johnson, M., Ulrich, B. Serre’s Condition R k for Sums of Geometric Links. Acta Math Vietnam 40, 393–401 (2015). https://doi.org/10.1007/s40306-015-0144-x

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  • DOI: https://doi.org/10.1007/s40306-015-0144-x

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