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arXiv · 2302.06592

A note on the supercritical deformed Hermitian-Yang-Mills equation

Junsheng Zhang
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Abstract

We show that on a compact K\"ahler manifold all real $(1,1)$-classes admitting solutions to the supercritical deformed Hermitian-Yang-Mills equation form a both open and closed subset of those which satisfy the numerical condition proposed by Collins-Jacob-Yau. More importantly, we show by examples that it can be a proper subset. This disproves a conjecture made by Collins-Jacob-Yau.

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Junsheng Zhang. 2023-02-13. A note on the supercritical deformed Hermitian-Yang-Mills equation. https://arxiv.org/abs/2302.06592

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