Cylinders in canonical del Pezzo fibrations
[Cylindres dans les fibrations canoniques de del Pezzo]
Sawahara, Masatomo1
1 Graduate School of Science and Engineering Saitama University Shimo-Okubo 255 Sakura-ku Saitama-shi Saitama 338-8570 (Japan)
Annales de l'Institut Fourier, Online first, 69 p.

Les cylindres dans les variétés projectives jouent un rôle important compte tenu du lien avec les actions de groupe unipotentes sur certaines variétés algébriques affines. Le travail précédent d’après Dubouloz et Kishimoto considère la condition avec laquelle une fibration de del Pezzo contient un cylindre vertical. Dans le travail présent, en tant que généralisation au niveau des singularités, nous déterminerons la condition sous laquelle une fibration de del Pezzo ayant des singularités canoniques admet un cylindre vertical tout en observant le degré et le type des singularités qui se trouvent sur la fibre générique correspondante.

Cylinders in projective varieties play an important role in connection with unipotent group actions on certain affine algebraic varieties. The previous work due to Dubouloz and Kishimoto deals with the condition for a del Pezzo fibration to contain a vertical cylinder. In the present work, as a generalization in the sense of singularities, we shall determine the condition under which a del Pezzo fibration with canonical singularities admits a vertical cylinder by means of degree and type of singularities found on the corresponding to the generic fiber.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3573
Classification : 14C20, 14E30, 14J17, 14J26, 14J45, 14R25
Keywords: Del Pezzo fibration, Cylinder, Generic fiber, Du Val singularity
Mot clés : Fibration de Del Pezzo, Cylindre, Fibre générique, Singularité de Du Val
Sawahara, Masatomo 1

1 Graduate School of Science and Engineering Saitama University Shimo-Okubo 255 Sakura-ku Saitama-shi Saitama 338-8570 (Japan) 
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Sawahara, Masatomo. Cylinders in canonical del Pezzo fibrations. Annales de l'Institut Fourier, Online first, 69 p.

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