On a Conjecture on the Variety of Lines on a Fano Complete Intersection
Abstract
The Debarrede 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.04713
 Bibcode:
 2020arXiv200204713C
 Keywords:

 Mathematics  Algebraic Geometry;
 14J45
 EPrint:
 6 pages, comments welcome!