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

José Carlos Sierra

doi:10.1016/j.crma.2013.09.016

Algebraic Geometry

Surfaces in

P^{4}

whose 4-secant lines do not sweep out a hypersurface

Presented by: Claire Voisin

José Carlos Sierra ¹

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

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

Abstract
Résumé

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.

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.

Received: 2013-07-09
Accepted: 2013-09-25
Published online: 2013-08-01

DOI: 10.1016/j.crma.2013.09.016

Author's affiliations:

José Carlos Sierra ¹

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

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     title = {Surfaces in $ {\mathbb{P}}^{4}$ whose 4-secant lines do not sweep out a hypersurface},
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José Carlos Sierra. Surfaces in $ {\mathbb{P}}^{4}$ whose 4-secant lines do not sweep out a hypersurface. Comptes Rendus. Mathématique, Volume 351 (2013) no. 15-16, pp. 623-625. doi : 10.1016/j.crma.2013.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.09.016/

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Cited by 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.

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