Rational surfaces in indexone Fano hypersurfaces
Abstract
We give the first evidence for a conjecture that a general, indexone, Fano hypersurface is not unirational: (i) a general point of the hypersurface is contained in no rational surface ruled, roughly, by lowdegree rational curves, and (ii) a general point is contained in no image of a Del Pezzo surface.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2006
 arXiv:
 arXiv:math/0601710
 Bibcode:
 2006math......1710B
 Keywords:

 Mathematics  Algebraic Geometry;
 14C05;
 14E08
 EPrint:
 13 pages, 6 diagrams