Singular lines of trilinear forms

@article{Draisma2009SingularLO,
  title={Singular lines of trilinear forms},
  author={J. Draisma and R. Shaw},
  journal={Linear Algebra and its Applications},
  year={2009},
  volume={433},
  pages={690-697}
}
  • J. Draisma, R. Shaw
  • Published 2009
  • Mathematics
  • Linear Algebra and its Applications
  • We prove that an alternating e-form on a vector space over a quasi-algebraically closed field always has a singular (e-1)-dimensional subspace, provided that the dimension of the space is strictly greater than e. Here an (e-1)-dimensional subspace is called singular if pairing it with the e-form yields zero. By the theorem of Chevalley and Warning our result applies in particular to finite base fields. Our proof is most interesting in the case where e=3 and the space has odd dimension n; then… CONTINUE READING
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