Corpus ID: 211083002

On a Conjecture on the Variety of Lines on a Fano Complete Intersection

@article{Canning2020OnAC,
  title={On a Conjecture on the Variety of Lines on a Fano Complete Intersection},
  author={Samir Canning},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
  • Samir Canning
  • Published 2020
  • Mathematics
  • arXiv: Algebraic Geometry
  • The Debarre-de Jong conjecture predicts that the Fano variety of lines on a smooth Fano hypersurface in $\mathbb{P}^n$ is always of the expected dimension. We generalize this conjecture to the case of Fano complete intersections and prove that for a Fano complete intersection $X\subset \mathbb{P}^n$ of hypersurfaces whose degrees sum to at most 7, the Fano variety of lines on $X$ has the expected dimension. 

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