Vol. 15, No. 4, 2022

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The deformed Hermitian Yang–Mills equation on three-folds

Vamsi Pritham Pingali

Vol. 15 (2022), No. 4, 921–935
Abstract

We prove an existence result for the deformed Hermitian Yang–Mills equation for the full admissible range of the phase parameter, i.e., $\stackrel{^}{𝜃}\in \left(\frac{\pi }{2},\frac{3\pi }{2}\right)$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path obtained by rewriting the equation as a generalised Monge–Ampère equation with mixed-sign coefficients.

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