Fano hypersurfaces and their birational geometry

2013/07/29 by de Fernex, Tommaso
#14B05 #14E05 #14N30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14E08 #Secondary: 14J45

paper · doi:10.48550/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.

Related

• On geometry of Fano threefold hypersurfaces
• Birational rigidity of singular Fano hypersurfaces
• Birationally rigid Fano varieties
• Effective birational rigidity of Fano double hypersurfaces
• Birational rigidity and K-stability of Fano hypersurfaces with ordinary double points