Hodge-Index Type Inequalities, Hyperbolic Polynomials, and Complex Hessian Equations

DOI10.1093/imrn/rnz159zbMath1487.32100arXiv1810.04662OpenAlexW2966734341WikidataQ127654708 ScholiaQ127654708MaRDI QIDQ5068193

Jian Xiao

Publication date: 5 April 2022

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04662

zbMATH Keywords

complex Hessian equationsHodge-index-type theorem

Mathematics Subject Classification ID

Compact Kähler manifolds: generalizations, classification (32J27) Other partial differential equations of complex analysis in several variables (32W50)

Related Items (4)

Complex Hessian equations with prescribed singularity on compact Kähler manifolds ⋮ Hodge-Riemann bilinear relations for Schur classes of ample vector bundles ⋮ On higher-rank Khovanskii-Teissier inequalities ⋮ Mixed Hodge-Riemann bilinear relations and \(m\)-positivity

Cites Work

• A form of Alexandrov-Fenchel inequality
• A numerical criterion for very ample line bundles
• Fully non-linear elliptic equations on compact Hermitian manifolds
• Numerical characterization of the Kähler cone of a compact Kähler manifold
• The mixed Hodge-Riemann bilinear relations for compact Kähler manifolds
• Liouville and Calabi-Yau type theorems for complex Hessian equations
• Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Notions of convexity
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