Rational surfaces in index-one Fano hypersurfaces

2006/01/29 by Beheshti, Roya, Starr, Jason Michael
#14C05 #14E08 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0601710

Abstract

We give the first evidence for a conjecture that a general, index-one, Fano hypersurface is not unirational: (i) a general point of the hypersurface is contained in no rational surface ruled, roughly, by low-degree rational curves, and (ii) a general point is contained in no image of a Del Pezzo surface.

Related

• Restrictions on rational surfaces lying in very general hypersurfaces
• Higher Fano manifolds and rational surfaces
• Rational curves in Fano hypersurfaces and tropical curves
• Rational Curves on Quasi-Projective Surfaces
• Stable rationality of index one Fano hypersurfaces containing a linear space