Stability of Equivariant Logarithmic Tangent Sheaves on Toric Varieties of Picard Rank Two

For an equivariant log pair \((X, D)\) where \(X\) is a normal toric variety and \(D\) a reduced Weil divisor, we study slope-stability of the logarithmic tangent sheaf \(\mathcal{T}_{X}(- \log D)\). We give a complete description of divisors \(D\) and polarizations \(L\) such that \(\mathcal{T}_{X}(- \log D)\) is (semi)stable with respect to \(L\) when \(X\) has a Picard rank one or two.