Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Varieties with one apparent double point

Authors: Ciro Ciliberto, Massimiliano Mella and Francesco Russo
Journal: J. Algebraic Geom. 13 (2004), 475-512
Published electronically: December 11, 2003
MathSciNet review: 2047678
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Abstract | References | Additional Information

Abstract: The number of apparent double points of a smooth, irreducible projective variety $X$ of dimension $n$ in ${\mathbb P}^{2n+1}$ is the number of secant lines to $X$ passing through the general point of ${\mathbb P}^{2n+1}$. This classical notion dates back to Severi. In the present paper we classify smooth varieties of dimension at most three having one apparent double point. The techniques developed for this purpose allow us to treat a wider class of projective varieties.

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Additional Information

Ciro Ciliberto
Affiliation: Dipartimento di Matematica, Universitá di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italia
MR Author ID: 49480

Massimiliano Mella
Affiliation: Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italia

Francesco Russo
Affiliation: Departamento de Matematica, Universidade Federal de Pernambuco, Cidade Universitaria, 50670-901 Recife–PE, Brasil
MR Author ID: 214972
ORCID: 0000-0002-5889-783X

Received by editor(s): January 24, 2002
Published electronically: December 11, 2003