For smooth projective toric varieties with a finite group action preserving the dense torus, equivariant unirationality is equivalent to the vanishing of the equivariant universal torsor obstruction class ∂(1_Pic(X)).
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Equivariant unirationality of toric varieties
For smooth projective toric varieties with a finite group action preserving the dense torus, equivariant unirationality is equivalent to the vanishing of the equivariant universal torsor obstruction class ∂(1_Pic(X)).