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

2023/02/13 by Zhang, Junsheng · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.06592

Abstract

We show that on a compact Kähler 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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