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Some criteria for positive forms and applications
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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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Cited by 2 Pith papers
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$p$-K\"ahler structures on nilmanifolds and holomorphically parallelizable manifolds
The Alessandrini–Bassanelli conjecture holds for nilmanifolds with nilpotent complex structures and for holomorphically parallelizable solvmanifolds, with low-degree classifications and new (n−2)-Kähler examples.
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p-K\"ahler structures on compact complex manifolds
On nilmanifolds with nilpotent or holomorphically parallelizable complex structures, p-Kähler structures are shown to imply (p+1)-Kähler (or balanced) structures, with new deformation obstructions and cohomological criteria.
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