Fano hypersurfaces and their birational geometry
arXiv:1307.7482
Abstract
We survey some results on the nonrationality and birational rigidity of certain hypersurfaces of Fano type. The focus is on hypersurfaces of Fano index one, but hypersurfaces of higher index are also discussed.
14 pages; v3: final version; to appear in the proceedings of the conference "Groups of Automorphisms in Birational and Affine Geometry", Levico Terme (Trento), 2012