Volume arithm\'etique de certains fibr\'es en droites hermitiens sur une vari\'et\'e torique lisse

Let $X$ be a smooth projective toric variety over $Spec(Z)$. Let $\overline{\mathcal{O}(D)}$ be an equivariant hermitian line bundle on $X$, equipped with a positive metric and invariant under the action of the compact torus of $X(C)$, we provide a formula for the arithmetic volume in term of Fenchel-Legendre transform attached to the metric.