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.
Varieties with a reducible hyperplane section whose two components are hypersurfaces / J.C. Sierra, A.L. Tironi. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 135:5(2007), pp. 1263-1269.
Varieties with a reducible hyperplane section whose two components are hypersurfaces
A.L. TironiUltimo
2007
Abstract
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.
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