Birational geometry of algebraic varieties with a pencil of Fano complete intersections

Details Birational geometry of algebraic varieties with a pencil of Fano complete intersections Birational geometry of algebraic varieties with a pencil of Fano complete intersections

2005-11-03

arxiv.org/abs/math/0511090v1

Mathematics

Algebraic Geometry

15 pages, LATEX

Scientific paper

We prove birational superrigidity of generic Fano fiber spaces $V/{\mathbb P}^1$, the fibers of which are Fano complete intersections of index 1 and dimension $M$ in ${\mathbb P}^{M+k}$, provided that $M\geq 2k+1$. The proof combines the traditional quadratic techniques of the method of maximal singularities with the linear techniques based on the connectedness principle of Shokurov and Koll\' ar. Certain related results are also considered.

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