Birationally rigid Fano hypersurfaces

Details Birationally rigid Fano hypersurfaces Birationally rigid Fano hypersurfaces

2002-01-30

arxiv.org/abs/math/0201302v2

Mathematics

Algebraic Geometry

31 pages, LATeX

Scientific paper

We prove that a smooth Fano hypersurface $V=V_M\subset{\Bbb P}^M$, $M\geq 6$, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov and Koll\' ar.

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