Quasitriviality of the Forms of Segre Varieties

Nikolay Zak

Quasitriviality of the Forms of Segre Varieties

Algebraic Geometry 2007-08-21 v1

Authors: Nikolay Zak

Abstract

We prove the rationality of a $\k$ -form $X$ of the product $S$ of projective spaces provided the existence of a $\k$ -point on $X$ . The method of the proof is to find a Galois-invariant birational projection of $S$ to the projective space. This method also allows to prove the quasitriviality of the forms of the hyperplane sections of some Segre varieties.

Keywords

Segre varieties rationality forms Galois-invariant birational projection projective spaces quasitriviality

Cite

@article{arxiv.0708.2492,
  title  = {Quasitriviality of the Forms of Segre Varieties},
  author = {Nikolay Zak},
  journal= {arXiv preprint arXiv:0708.2492},
  year   = {2007}
}

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