Rational surfaces in index-one Fano hypersurfaces

@article{Beheshti2006RationalSI,
  title={Rational surfaces in index-one Fano hypersurfaces},
  author={Roya Beheshti and J. Starr},
  journal={Journal of Algebraic Geometry},
  year={2006},
  volume={17},
  pages={255-274}
}
  • Roya Beheshti, J. Starr
  • Published 2006
  • Mathematics
  • Journal of Algebraic Geometry
  • 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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