Year: 2025
Type: preprint
Abstract: We introduce a new Hermitian metric on the cohomology ring of compact Kählerian manifolds with a pair $(v,w)$ satisfying certain Hodge-Riemann relations. An Hermitian metric on the exterior algebra of the cotangent bundle is also defined and we establish the corresponding theory of harmonic forms, relating the global metric and local metric. This generalizes the classical Hodge theory. As an immediate application we give a new proof of Dinh-Nguyen's theorem on the Hodge-Riemann relations for mixed Kähler classes. We give several other applications to the Lefschetz property and Hodge-Riemann relations of Chern classes of ample vector bundles.
Source: arXiv (Cornell University)
Author: Lin, Yiran
Institution: Tsinghua University
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417458459
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