LCK metrics on toric LCS manifolds.

We show a bijective correspondence between compact toric locally conformally symplectic manifolds which admit a compatible complex structure and pairs (C , a) , where C is a good cone in the dual Lie algebra of the torus and a is a positive real number. Moreover, we prove that any toric locally conformally Kähler metric on a compact manifold admits a positive potential. [ABSTRACT FROM AUTHOR]