Local existence of solutions to polynomial curvature equations is equivalent to local polystability, with local filtrations and a Kempf-Ness homeomorphism.
The supercritical deformed Hermitian Yang--Mills equation on compact projective manifolds
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In this paper, we extend a result of Gao Chen regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler manifolds to allow for the twisting function to be non-constant and slightly negative in all dimensions. Using this result, we prove that the twisted supercritical dHYM equation on compact, projective manifolds can be solved provided certain numerical conditions are satisfied.
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Perturbations of Vector Bundle whose Curvature Form Solves a Polynomial Equation
Local existence of solutions to polynomial curvature equations is equivalent to local polystability, with local filtrations and a Kempf-Ness homeomorphism.