Surfaces in $ {\mathbb{P}}^{4}$ whose 4-secant lines do not sweep out a hypersurface

Sierra, José Carlos

doi:10.1016/j.crma.2013.09.016

Algebraic Geometry

Surfaces in

P^{4}

whose 4-secant lines do not sweep out a hypersurface
[Surfaces de

P^{4}

dont les droites quadrisécantes ne couvrent pas une hypersurface]

Présenté par : Claire Voisin

Sierra, José Carlos ¹

¹ Instituto de Ciencias Matemáticas (ICMAT), Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain

Comptes Rendus. Mathématique, Tome 351 (2013) no. 15-16, pp. 623-625.

Résumé
Abstract

Nous montrons quʼune surface lisse dans $P^{4}$ dont les droites quadrisécantes ne couvrent pas une hypersurface de $P^{4}$ est, soit contenue dans un pinceau de cubiques, soit liée à une surface de Veronese via lʼintersection complète dʼune cubique et dʼune quartique.

We prove that a smooth surface in $P^{4}$ whose 4-secant lines do not sweep out a hypersurface of $P^{4}$ either lies on a pencil of cubic hypersurfaces, or else is linked to a Veronese surface by the complete intersection of a cubic and a quartic hypersurface.

Reçu le : 2013-07-09
Accepté le : 2013-09-25
Publié le : 2013-08-01

DOI : 10.1016/j.crma.2013.09.016

Affiliations des auteurs :

Sierra, José Carlos ¹

¹ Instituto de Ciencias Matemáticas (ICMAT), Consejo Superior de Investigaciones Científicas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain

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Sierra, José Carlos. Surfaces in $ {\mathbb{P}}^{4}$ whose 4-secant lines do not sweep out a hypersurface. Comptes Rendus. Mathématique, Tome 351 (2013) no. 15-16, pp. 623-625. doi : 10.1016/j.crma.2013.09.016. http://www.numdam.org/articles/10.1016/j.crma.2013.09.016/

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Cité par Sources :

^☆ Research supported by the “Ramón y Cajal” contract RYC-2009-04999 of MICINN, the project MTM2012-32670 and the ICMAT “Severo Ochoa” project SEV-2011-0087 of MINECO.