Deformation of a generically finite map to a hypersurface embedding

2017/08/25 by Catanese, Fabrizio, Lee, Yongnam
#14D15 #14J15 #14J70 #14K12 #32G05 #32G10 #32H02 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.07745

Abstract

Motivated by the theory of Inoue-type varieties, we give a structure theorem for projective manifolds W₀ with the property of admitting a 1-parameter deformation where W_t is a hypersurface in a projective smooth manifold Z_t. 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 Z_t is projective space, respectively an Abelian variety.

Related

• Subvarieties of generic hypersurfaces in any variety
• Deformations of canonical double covers
• Deformations of canonical triple covers
• Global deformations of certain rational almost homogeneous projective bundles
• An infinitesimal condition to deform a finite morphism to an embedding