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Varieties with a reducible hyperplane section whose two components are hypersurfaces

Authors:	José Carlos Sierra Andrea Luigi Tironi

Institution:	Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain ; Dipartimento di Matematica ``F. Enriques", Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

Abstract:	We classify smooth complex projective varieties $X\subset\mathbb{P}^N$ of dimension $n\geq 2$ admitting a divisor of the form among their hyperplane sections, both and of codimension $\leq 1$ in their respective linear spans. In this setting, one of the following holds: 1) is either the Veronese surface in $\mathbb{P}^5$ or its general projection to $\mathbb{P}^4$ , 2) $n\leq 3$ and $X\subset{\mathbb{P}}^{n+2}$ is contained in a quadric cone of rank or , 3) and $X\subset\mathbb{P}^3$ .

Keywords:	Algebraic geometry reducible hyperplane sections of varieties

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