The supercritical deformed Hermitian Yang--Mills equation on compact projective manifolds

Abstract

In this paper, we extend a result of [Che21] regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact Kähler manifolds to allow for the twisting function to be non-constant and slightly negative in all dimensions. Using this result along with the methods in [DP20], we prove that the twisted dHYM equation on compact, projective manifolds can be solved provided certain numerical conditions are satisfied. As a corollary, we obtain a new proof in the projective case of a recent theorem of [CLT21] addressing a conjecture of [CJY20].