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Generalization of a connectedness result to cohomologically complete intersections

Hellus, Michael



Abstract

It is a well-known result from Hartshorne that, in projective space over a field, every set-theoretical complete intersection of positive dimension is connected in codimension one. Another important connectedness result (also from Hartshorne) is that a local ring with disconnected punctured spectrum has depth at most 1. The two results are related; Hartshorne calls the latter "the keystone to the ...

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