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On the birational geometry of toric Fano 4-folds

Cinzia Casagrande
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Abstract

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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Cinzia Casagrande. 2001-04-23. On the birational geometry of toric Fano 4-folds. https://arxiv.org/abs/math/0104210

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