Is there an example of a smooth projective hypersurface in $\mathbb{P}^n_k$ ($k=\overline{k}$) that does not contain any projective toric varieties (edit: of positive dimension)? Or is it the case that every such hypersurface will contain a projective toric varityvariety (edit: of positive dimension)?
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Do projective hypersurfaces contain projective toric varieties?Is there an example of a smooth projective hypersurface in $\mathbb{P}^n_k$ ($k=\overline{k}$) that does not contain any projective toric varieties? Or is it the case that every such hypersurface will contain a projective toric varity?
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