Deformation of a generically finite map to a hypersurface embedding

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We give a structure theorem for projective manifolds W-0 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 W-0. We give applications to the case where Z(t) is projective space, respectively an Abelian variety. (C) 2018 Published by Elsevier Masson SAS.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2019-05
Language
English
Article Type
Article
Citation

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v.125, pp.175 - 188

ISSN
0021-7824
DOI
10.1016/j.matpur.2018.06.024
URI
http://hdl.handle.net/10203/262110
Appears in Collection
MA-Journal Papers(저널논문)
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