Abstract

We give a structure theorem for projective manifolds W0 with the property of admitting a 1-parameter deformation where Wt is a hypersurface in a projective smooth manifold Zt.Their structure is the one of special iterated univariate coverings which we call of normal type, which essentially means that the line bundles where the univariate coverings live are tensor powers of the normal bundle to the image X of W0.We give applications to the case where Zt is projective space, respectively an Abelian variety.

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