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arXiv · 2502.17317

Some criteria for positive forms and applications

Filippo Fagioli·Asia Mainenti
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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 $\mathbb{C}^4$. 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.

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Filippo Fagioli, Asia Mainenti. 2025-02-24. Some criteria for positive forms and applications. https://arxiv.org/abs/2502.17317

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