## The density of rational lines on cubic hypersurfaces

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- by Scott T. Parsell
- Trans. Amer. Math. Soc.
**352**(2000), 5045-5062 - DOI: https://doi.org/10.1090/S0002-9947-00-02635-0
- Published electronically: July 18, 2000
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## Abstract:

We provide a lower bound for the density of rational lines on the hypersurface defined by an additive cubic equation in at least $57$ variables. In the process, we obtain a result on the paucity of non-trivial solutions to an associated system of Diophantine equations.## References

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## Bibliographic Information

**Scott T. Parsell**- Affiliation: Department of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor, Michigan 48109-1109
- Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- Email: parsell@alum.mit.edu
- Received by editor(s): May 21, 1999
- Received by editor(s) in revised form: July 23, 1999
- Published electronically: July 18, 2000
- Additional Notes: Research supported in part by NSF grant DMS-9622773 and by a fellowship from the David and Lucile Packard Foundation.
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 5045-5062 - MSC (2000): Primary 11D25, 11D45, 11L03, 11P55
- DOI: https://doi.org/10.1090/S0002-9947-00-02635-0
- MathSciNet review: 1778504