Detaching embedded points

@article{Chen2012DetachingEP,
  title={Detaching embedded points},
  author={Dawei Chen and Scott Nollet},
  journal={Algebra \& Number Theory},
  year={2012},
  volume={6},
  pages={731-756}
}
Suppose that XYP N differ at finitely many points: when is Y a flat limit of X union isolated points? Our main result says that this is possible when X is a local complete intersection of codimension 2 and the multiplicities are at most 3. We show by example that no hypothesis can be weakened: the conclusion fails for (a) embedded points of multiplicity > 3, (b) local complete intersections X of codimension > 2 and (c) non-local complete intersections of codimension 2. As applications, we… 
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