On the birational geometry of toric Fano 4-folds

Mathematics – Algebraic Geometry

Scientific paper

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6 pages, contains an abridged French version

Scientific paper

We announce a factorization result for equivariant birational morphisms
between toric 4-folds whose source is Fano: such a morphism is always a
composite of blow-ups along smooth invariant centers. Moreover, we show with a
counterexample that, differently from the 3-dimensional case, even if both
source and target are Fano, the intermediate varieties can not be chosen Fano.

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