Varieties with a reducible hyperplane section whose two components are hypersurfaces
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- by José Carlos Sierra and Andrea Luigi Tironi PDF
- Proc. Amer. Math. Soc. 135 (2007), 1263-1269 Request permission
Abstract:
We classify smooth complex projective varieties $X\subset \mathbb {P}^N$ of dimension $n\geq 2$ admitting a divisor of the form $A+B$ among their hyperplane sections, both $A$ and $B$ of codimension $\leq 1$ in their respective linear spans. In this setting, one of the following holds: 1) $X$ 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 $3$ or $4$, 3) $n=2$ and $X\subset \mathbb {P}^3$.References
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Additional Information
- José Carlos Sierra
- Affiliation: Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain
- Email: jcsierra@mat.ucm.es
- Andrea Luigi Tironi
- Affiliation: Dipartimento di Matematica “F. Enriques", Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
- MR Author ID: 677961
- Email: atironi@mat.unimi.it
- Received by editor(s): January 21, 2005
- Received by editor(s) in revised form: December 6, 2005
- Published electronically: November 13, 2006
- Additional Notes: This work was done in the framework of the National Research Project “Geometry on Algebraic Varieties”, supported by the MIUR of the Italian Government (Cofin 2002).
- Communicated by: Michael Stillman
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1263-1269
- MSC (2000): Primary 14C20; Secondary 14N05
- DOI: https://doi.org/10.1090/S0002-9939-06-08637-0
- MathSciNet review: 2276633