Proposition 5.21 . [02TG]

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Proposition 5.21.

The canonical metric is compatible with the tensor product of line bundles.

(1)

Let $L_{i}$ , $i=1,2$ , be toric line bundles. Then ${\overline{L_{1}\otimes L_{2}}}^{{\operatorname{can}}}={\overline{L_{1}}}^{{\operatorname{can}}}\otimes{\overline{L_{2}}}^{{\operatorname{can}}}$ .
(2)

Let $L$ be a toric line bundle. Then ${\overline{L^{-1}}}^{{\operatorname{can}}}=({\overline{L}}^{{\operatorname{can}}})^{-1}$ .