Birationally rigid Fano fibre spaces. II
Abstract
We prove the birational rigidity of large classes of FanoMori fibre spaces over a base of arbitrary dimension bounded above by a constant that depends only on the dimension of the fibres. To do this, we first show that if every fibre of a FanoMori fibre space satisfies certain natural conditions, then every birational map onto another such space is fibrewise. Then we construct large classes of fibre spaces (whose fibres are either Fano double spaces of index 1 or Fano hypersurfaces of index 1) satisfying these conditions.
 Publication:

Izvestiya: Mathematics
 Pub Date:
 August 2015
 DOI:
 10.1070/IM2015v079n04ABEH002762
 arXiv:
 arXiv:1407.0687
 Bibcode:
 2015IzMat..79..809P
 Keywords:

 Mathematics  Algebraic Geometry;
 14E05;
 14E07;
 14E08
 EPrint:
 31 pages