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When the union of two varieties in projective space is a complete
intersection, we say they are linked. The equivalence relation generated
by successive linkages is called liaison. This relation has been very
useful in the classification problem for curves in projective three-space,
and more generally for codimension two subschemes of any projective space.
In this talk we describe a generalization of this notion, called
Gorenstein liaison, which seems to be the appropriate corresponding
concept for varieties of codimension at least 3 in projective spaces.
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