Positivity of Smooth Currents on Singular Spaces

Duc-Thai Do; Duc-Viet Vu

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arXiv · 2609.04335

Positivity of Smooth Currents on Singular Spaces

Duc-Thai Do·Duc-Viet Vu

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Abstract

We study two notions of positivity for smooth currents on singular spaces. We show that they are not equivalent by establishing a necessary condition on the fourth Whitney cones. We also construct an explicit compact normal projective variety $X$ and a real smooth $(1,1)$-form $T$ on $X$ such that $T$ has local smooth ddc-potentials and is a K\"ahler current, but $T$ is not a positive form (hence not Hermitian).

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Duc-Thai Do, Duc-Viet Vu. 2026-09-03. Positivity of Smooth Currents on Singular Spaces. https://arxiv.org/abs/2609.04335

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