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Toric variety is embedding of algebraic tori.

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Toric structures on projective space

There is an effective Hamiltonian $T=(S^1)^r$ action on $\mathbb{P}^n$, with $2^r=n+1$. Such actions appear in quantum information theory! Please see Lemma (3.1) in http://arxiv.org/abs/1506.05516 for …
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