The deformed Hermitian Yang–Mills equation on three-folds

Abstract

We prove an existence result for the deformed Hermitian Yang–Mills equation for the full admissible range of the phase parameter, i.e., $\widehat{𝜃}\in (\frac{\pi }{2},\frac{3\pi }{2})$, 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.