Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fu, Jixiang, Li, Xuan, Zhang, Dekai, Zhang, Ziyi
Institution: Fudan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215070424