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., 𝜃^ (π 2 , 3π 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.

Keywords
deformed Hermitian–Yang–Mills equation, generalised Monge–Ampère equation, special Lagrangian equation
Mathematical Subject Classification 2010
Primary: 32Q15, 53C07
Milestones
Received: 4 October 2019
Revised: 5 November 2020
Accepted: 31 December 2020
Published: 3 September 2022
Authors
Vamsi Pritham Pingali
Department of Mathematics
Indian Institute of Science
Bangalore
India