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Rational surfaces in index-one Fano hypersurfaces

Roya Beheshti·Jason Michael Starr
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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.

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Roya Beheshti, Jason Michael Starr. 2006-01-29. Rational surfaces in index-one Fano hypersurfaces. https://arxiv.org/abs/math/0601710

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