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Toric variety is embedding of algebraic tori.
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the map on Picard groups induced by restriction to a toric subvariety
A toric Cartier divisor $D$ is given by the Cartier data $\{m_\sigma\}_{\sigma \in \Sigma}$ [CLS, Theorem 4.2.8] where for each affine open chart $U_\sigma$, the toric coordinate $x^{-m_\sigma}$ is th …