Flips from 4-folds with isolated complete intersection singularities whose downstairs have rational bi-elephants

Details Flips from 4-folds with isolated complete intersection singularities whose downstairs have rational bi-elephants Flips from 4-folds with isolated complete intersection singularities whose downstairs have rational bi-elephants

1996-06-12

arxiv.org/abs/alg-geom/9606011v1

Mathematics

Algebraic Geometry

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Scientific paper

We shall investigate a flipping contraction g : X -> Y from a 4-fold X with at most isolated complete intersection singularities. If Y has an anti-bi-canonical divisor (=bi-elephant) with only rational singularities, then g carries an inductive structure chained up by blow-ups (La Torre Pendente), and in particular the flip exists. This naturally contains Miles Reid's `Pagoda' as an anti-canonical divisor (=elephant) and its proper transforms.

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