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arXiv · 2105.10725

A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation

Jianchun Chu·Man-Chun Lee·Ryosuke Takahashi
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Abstract

The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact K\"ahler manifolds that corresponds to the special Lagrangian equation in the context of the Strominger-Yau-Zaslow mirror symmetry. Recently, Chen proved that the existence of the solution is equivalent to a uniform stability condition in terms of holomorphic intersection numbers along test families. In this paper, we establish an analogous stability result not involving a uniform constant in accordance with a recent work on the $J$-equation by Song, which makes further progress toward Collins-Jacob-Yau's original conjecture in the supercritical phase case. In particular, we confirm this conjecture for projective manifolds in the supercritical phase case.

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Jianchun Chu, Man-Chun Lee, Ryosuke Takahashi. 2021-05-22. A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation. https://arxiv.org/abs/2105.10725

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