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A note on the supercritical deformed Hermitian-Yang-Mills equation
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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.
Forward citations
Cited by 2 Pith papers
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A numerical criterion for complex Hessian type equations on projective manifolds
Existence of solutions to complex Hessian-type equations on projective manifolds is equivalent to uniform positivity of certain subvariety integrals when the associated polynomial is strictly right-Noetherian.
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Deformed Hermitian-Yang-Mills equation on the manifold of full flags
First irreducible rank-2 dHYM connections are constructed on the full flag manifold F₂, and rank-1 solutions outside the supercritical regime disprove conjectured stability conditions.
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