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Factorisation faible des applications birationnelles [d'après Abramovich, Karu, Matsuki, Włodarczyk et Morelli]

Laurent Bonavero
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Abstract

Dans cet exposé, nous expliquons le résultat suivant démontré récemment par Abramovich, Karu, Matsuki et Włodarczyk : toute application birationnelle entre deux variétés algébriques complètes et lisses sur un corps algébriquement clos de caractéristique nulle se factorise en une suite finie d'éclatements et de contractions de centres lisses. Ce résultat n'aurait sans doute pas vu le jour sans la démonstration de son analogue dans le cadre de la géométrie torique par Morelli et Włodarczyk au milieu des années 90. La démonstration donnée par Abramovich, Karu, Matsuki et Włodarczyk est une réduction au cas torique, nous en donnons les grandes étapes.

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Laurent Bonavero. 2000-11-08. Factorisation faible des applications birationnelles [d'après Abramovich, Karu, Matsuki, Włodarczyk et Morelli]. https://arxiv.org/abs/math/0011043

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