Some criteria for positive forms and applications

2025/02/24 by Fagioli, Filippo, Mainenti, Asia · 2 citations
#15A63 (Primary) 15B57 #32U40 (Secondary) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.17317

Abstract

The aim of this paper is to gain a better understanding of weak and strong positivity for exterior forms on complex vector spaces. We prove a dimensionality reduction argument for positive forms, which allows us to restrict to the case of (2,2)-forms in ℂ⁴. In this setting, we find criteria for weak positivity based on the associated Hermitian matrix. As an application we prove, by duality, the strong positivity of some families of (2,2)-forms, already of interest in works by other authors.

Cited by

• p-Kähler structures on nilmanifolds and holomorphically parallelizable manifolds
• p-Kähler structures on compact complex manifolds

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