Quasitriviality of the Forms of Segre Varieties
2007
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.
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