  The vector space of holomorphic polyvector fields on any complex manifold has
a natural Gerstenhaber algebra structure. In this paper, we study BV operators
of the Gerstenhaber algebras of holomorphic polyvector fields on smooth compact
toric varieties. We give a necessary and sufficient condition for the existence
of BV operators of the Gerstenhaber algebra of holomorphic polyvector fields on
any smooth compact toric variety.
