The Existence of Gorenstein terminal fourfold flips

Details The Existence of Gorenstein terminal fourfold flips The Existence of Gorenstein terminal fourfold flips

1999-05-12

arxiv.org/abs/math/9905067v2

Mathematics

Algebraic Geometry

We should add the paper [Si] to the reference

Scientific paper

This is a revised version of my paper which appeared in J. Math. Sci. Univ. Tokyo. We prove that for a flipping contraction from a Gorenstein terminal 4-fold, the pull back of a general hyperplane section of the down-stair has only canonical singularities. Based on this fact and using Siu-Kawamata-Nakayama's extension theorem [Si], [Kaw4], [Kaw5] and [Nak2], we prove the existence of the flip of such a flipping contraction. Furthermore we classify such flipping contractions and the flips under some additional assumptions.

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