Let $\{\alpha\}$ and $\{\beta\}$ be nef cohomology classes of bidegree $(1,\,1)$ on a compact $n$-dimensional K\"ahler manifold $X$ such that the difference of intersection numbers $\{\alpha\}^n - n\,\{\alpha\}^{n-1}.\,\{\beta\}$ is positive. We solve in a number of special but rather inclusive cases the quantitative part of Demailly's Transcendental Morse Inequalities Conjecture for this context predicting the lower bound $\{\alpha\}^n-n\,\{\alpha\}^{n-1}.\,\{\beta\}$ for the volume of the difference class $\{\alpha-\beta\}$... (read more)

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