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arXiv · 2608.30153

Transcendental Morse inequality on K\"ahler manifolds

Valentino Tosatti
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Abstract

We prove the transcendental Morse inequality conjecture of Boucksom-Demailly-P\u{a}un-Peternell. Among the corollaries of this result, this proves orthogonality of divisorial Zariski decompositions, shows that the pseudoeffective and movable cones are dual, and establishes the differentiability of the volume function on the big cone, on all compact K\"ahler manifolds.

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Valentino Tosatti. 2026-08-31. Transcendental Morse inequality on K\"ahler manifolds. https://arxiv.org/abs/2608.30153

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