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Subvarieties of generic hypersurfaces in any variety

Subvarieties of generic hypersurfaces in any variety

The geometry of a desingularization Ym of an arbitrary subvariety of a generic hypersurface Xn in an ambient variety W (e.g. W = ℙn+1) has received much attention over the past decade or so. Clemens [5] has proved that for m = 1, n = 2, W = ℙ3 and …