Comptes Rendus
no. 2
Algebraic geometry
Brill–Noether general curves on Knutsen K3 surfaces
[Courbes générales au sens de Brill–Noether sur les surfaces K3 de Knutsen]

Présenté par : Claire Voisin

Maxim Arap1 ; Nicholas Marshburn1
1 Department of Mathematics, 404 Krieger Hall, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA
Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 133-135.

Cet article classifie les surfaces K3 de Knutsen dont toutes les sections hyperplanes sont irréductibles et réduites. Comme application, on obtient des familles infinies de surfaces K3 de nombre de Picard 2 dont les sections hyperplanes générales sont des courbes générales au sens de la théorie de Brill–Noether.

This article classifies Knutsen K3 surfaces all of whose hyperplane sections are irreducible and reduced. As an application, this gives infinite families of K3 surfaces of Picard number two whose general hyperplane sections are Brill–Noether general curves.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.020
Maxim Arap 1 ; Nicholas Marshburn 1

1 Department of Mathematics, 404 Krieger Hall, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA 
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Maxim Arap; Nicholas Marshburn. Brill–Noether general curves on Knutsen K3 surfaces. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 133-135. doi : 10.1016/j.crma.2013.11.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.020/

[1] M. Arap; J. Cutrone; N. Marshburn On the existence of certain weak Fano threefolds of Picard number two | arXiv

[2] A.L. Knutsen Smooth curves on projective K3 surfaces, Math. Scand., Volume 90 (2002), pp. 215-231

[3] A.L. Knutsen Smooth, isolated curves in families of Calabi–Yau threefolds in homogeneous spaces, J. Korean Math. Soc., Volume 50 (2013) no. 5, pp. 1033-1050

[4] R. Lazarsfeld Brill–Noether–Petri without degenerations, J. Differ. Geom., Volume 23 (1986) no. 3, pp. 299-307

[5] S. Mukai New development of theory of Fano 3-folds: vector bundle method and moduli problem, Sūgaku, Volume 47 (1995) no. 2, pp. 125-144 (translation in: Sūgaku Expo., 15, 2, 2002, pp. 125-150)

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