Rational surfaces in index-one Fano hypersurfaces
classification
🧮 math.AG
keywords
generalrationalcontainedfanohypersurfaceindex-onepointsurface
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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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