Study On The Existion Of The Flip Of Contraction Of Higher Dimensional Projective Algebraic Varieties

Minimal model problem for higher dimensional projectivevarieties is one of the main stream problem on algebraic geometry, of which the most difficult part is to prove the Flip Conjecture. It has been one of the most attractive reseach problems in mathematics to prove the Flip Conjective for higher dimensional projective varieties. Since Mori completed proof of the Flip Conjecture for three dimensional projective varieties in 1988 and obtained the Fields Medal in 1990. In this paper, the main aim is to study the Flip Conjecture for higher dimensionalprojective varieties. It is proved that let f:X→Y be a smallcontraction of smooth projective varieties of dimension n≥4 . If the exceptional locus is n-2 dimensional projective space, the flipf~+ :X~+ → Y exists for f.