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arXiv · 2609.40238

Nakai-Moishezon type criteria for Hessian type equations on compact Kähler manifolds

Jixiang Fu·Xuan Li·Dekai Zhang·Ziyi Zhang
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Abstract

We establish numerical criteria for polynomial positivity of real $(1,1)$-classes on compact Kähler manifolds for strictly right-Noetherian polynomials. As applications, we obtain existence and uniqueness for the generalized Monge-Ampère equations with a smooth zeroth coefficient, the complex Hessian and Hessian quotient equations, and the critical LYZ equation. We also characterize the cone of $k$-positive classes as a connected component of a numerical positivity cone.

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Jixiang Fu, Xuan Li, Dekai Zhang, Ziyi Zhang. 2026-09-30. Nakai-Moishezon type criteria for Hessian type equations on compact Kähler manifolds. https://arxiv.org/abs/2609.40238

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