Irreducible components of Toric Complete Intersections

An equivariant linear system on a toric variety is a linear system invariant under the torus action. We study the number of irreducible components of the complete intersection of general divisors from a fixed collection of equivariant linear system on a toric variety $X$. An explicit formula for the number of components was obtained by Khovanskii in 2016 for the case $X=T^n$ over $\mathbb{C}$ and generalized to an algebraically closed field of arbitrary characteristic the author in 2024. Building on these results, we give a recursive formula for an arbitrary toric variety.