Rational surfaces in index-one Fano hypersurfaces

Details Rational surfaces in index-one Fano hypersurfaces Rational surfaces in index-one Fano hypersurfaces

2006-01-29

arxiv.org/abs/math/0601710v1

Mathematics

Algebraic Geometry

13 pages, 6 diagrams

Scientific paper

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.

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