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

Abstract

In this paper, we extend a result of Chen regarding the solvability of the twisted deformed Hermitian Yang–Mills (dHYM) equations on compact Kähler manifolds to allow for the twisting function to be nonconstant and slightly negative in all dimensions. Using this result along with the methods of Datar and Pingali, 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 Chu, Lee, and Takahashi addressing a conjecture of Collins, Jacob, and Yau.