Projective invariant Demazure models

This paper gives a detailed exposition of the construction of models of tori that are not decomposable over the base field. The presence of a finite number of nonconjugate subgroups in the group $\operatorname{GL}(n,\mathbf Z)$ enables one to classify the tori of given dimension by the Bravais type of their modules of rational characters. A quite complete description of projective Demazure models in low dimensions is given. The rationality of tori with cubic character lattices is proved.
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