A counterexample to the zero-mass conjecture

Long Li; Mingchen Xia

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arXiv · 2607.26549

A counterexample to the zero-mass conjecture

Long Li·Mingchen Xia

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Abstract

We construct an explicit negative plurisubharmonic function on the unit polydisk in $\mathbb{C}^n, n\geq 2$ with an isolated singularity at the origin. Its Monge-Amp\`{e}re measure is the Dirac mass at the origin, but its Lelong number vanishes. This gives a negative answer to the zero-mass conjecture of Guedj-Rashkovskii in every complex dimension at least two.

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Long Li, Mingchen Xia. 2026-07-29. A counterexample to the zero-mass conjecture. https://arxiv.org/abs/2607.26549

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