Quasitriviality of the Forms of Segre Varieties
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2007
- DOI:
- 10.48550/arXiv.0708.2492
- arXiv:
- arXiv:0708.2492
- Bibcode:
- 2007arXiv0708.2492Z
- Keywords:
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- Mathematics - Algebraic Geometry