We study positivity in the conjecture proposed by Lejmi and Sz\'{ e}kelyhidi on finding effective necessary and sufficient conditions for solvability of the inverse $\sigma_k$ equation, or equivalently, for convergence of the inverse $\sigma_k$-flow. In particular, for the inverse $\sigma_{ n-1}$-flow we partially verify their conjecture by obtaining the desired positivity for $(n-1, n-1)$ cohomology classes. As an application, we also partially verify their conjecture for 3-folds.
Categories: math.DG math.AG