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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{fu2026nakaimoishezon,
  title = {{Nakai-Moishezon type criteria for Hessian type equations on compact Kähler manifolds}},
  author = {Jixiang Fu and Xuan Li and Dekai Zhang and Ziyi Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.40238},
  eprint = {2609.40238},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.40238},
}
RIS
TY  - UNPB
TI  - Nakai-Moishezon type criteria for Hessian type equations on compact Kähler manifolds
AU  - Jixiang Fu
AU  - Xuan Li
AU  - Dekai Zhang
AU  - Ziyi Zhang
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.40238
UR  - https://arxiv.org/abs/2609.40238
AB  - 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.
ER  -