We classify smooth complex projective varieties X ⊂ P^N of dimension n ≥ 2 admitting a divisor of the form A+B among their hyperplane sections, both A and B of codimension ≤ 1 in their respective linear spans. In this setting, one of the following holds: 1) X is either the Veronese surface in P^5 or its general projection to P^4, 2) n ≤ 3 and X ⊂ P^n+2 is contained in a quadric cone of rank 3 or 4, 3) n = 2 and X ⊂ P^3.
|Titolo:||Varieties with a reducible hyperplane section whose two components are hypersurfaces|
TIRONI, ANDREA LUIGI (Ultimo)
|Parole Chiave:||Algebraic geometry; Reducible hyperplane sections of varieties|
|Data di pubblicazione:||2007|
|Digital Object Identifier (DOI):||10.1090/S0002-9939-06-08637-0|
|Appare nelle tipologie:||01 - Articolo su periodico|