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manuscripta mathematica

, Volume 121, Issue 4, pp 491–526 | Cite as

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

  • Aleksandr V. PukhlikovEmail author
Article

Abstract

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 ≥ 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 Kollár. Certain related results are also considered.

Keywords

Complete Intersection Algebraic Variety Exceptional Divisor Maximal Singularity Fano Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK

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