Explicit biregular/birational geometry of affine threefolds: completions of A^3 into del Pezzo fibrations and Mori conic bundles

Abstract : We study certain pencils of del Pezzo surfaces generated by a smooth del Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a weighted projective space P and an appropriate multiple of a hyperplane H. Our main observation is that every minimal model program relative to the morphism lifting such pencil on a suitable resolution of its indeterminacies preserves the open subset P \ H ≃ A^3. As an application, we obtain projective completions of A^3 into del Pezzo fibrations over P^1 of every degree less or equal to 4. We also obtain completions of A^3 into Mori conic bundles, whose restrictions to A^3 are twisted C*-fibrations over A^2 .
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01183351
Contributeur : Adrien Dubouloz <>
Soumis le : vendredi 7 août 2015 - 12:29:46
Dernière modification le : mercredi 23 septembre 2015 - 14:34:38
Document(s) archivé(s) le : mercredi 26 avril 2017 - 10:07:55

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DelPezzo-Completions.pdf
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  • HAL Id : hal-01183351, version 1
  • ARXIV : 1508.01792

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Adrien Dubouloz, Takashi Kishimoto. Explicit biregular/birational geometry of affine threefolds: completions of A^3 into del Pezzo fibrations and Mori conic bundles. 2015. <hal-01183351>

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