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

@inproceedings{Ballal2021TheSD, title={The supercritical deformed Hermitian Yang--Mills equation on compact projective manifolds}, author={A. K. Ballal}, year={2021} }

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…

## References

SHOWING 1-10 OF 20 REFERENCES

### A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation

- Mathematics
- 2021

The deformed Hermitian–Yang–Mills equation is a complex Hessian equation on compact Kähler manifolds that corresponds to the special Lagrangian equation in the context of the Strominger–Yau–Zaslow…

### The deformed Hermitian Yang–Mills equation on three-folds

- MathematicsAnalysis & PDE
- 2022

We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $\hat{\theta} \in (\frac{\pi}{2},\frac{3\pi}{2})$, on compact…

### The J-equation and the supercritical deformed Hermitian–Yang–Mills equation

- Mathematics
- 2020

In this paper, we provide a necessary and sufficient condition for the solvability of the supercritical deformed Hermitian-Yang-Mills equation using integrals on subvarieties. This result confirms…

### The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics

- MathematicsGeometry and Physics: Volume I
- 2018

This chapter provides an introduction to the mathematics and physics of the deformed Hermitian–Yang–Mills equation, a fully non-linear geometric PDE on Kähler manifolds, which plays an important role…

### A numerical criterion for generalised Monge-Ampère equations on projective manifolds

- MathematicsGeometric and Functional Analysis
- 2021

We prove that generalised Monge-Ampere equations (a family of equations which includes the inverse Hessian equations like the J-equation, as well as the Monge-Ampere equation) on projective manifolds…

### On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*

- Mathematics
- 1978

Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent the…

### Fully non-linear elliptic equations on compact Hermitian manifolds

- MathematicsJournal of Differential Geometry
- 2018

We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific…

### On a class of fully nonlinear flows in Kähler geometry

- Mathematics
- 2009

Abstract In this paper, we study a class of fully nonlinear metric flows on Kähler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long…

### Nakai-Moishezon criterions for complex Hessian equations

- Mathematics
- 2020

The $J$-equation proposed by Donaldson is a complex Hessian quotient equation on Kahler manifolds. The solvability of the $J$-equation is proved by Song-Weinkove to be equivalent to the existence of…

### GEOMETRIC ASPECTS OF THE THEORY OF FULLY NON LINEAR ELLIPTIC EQUATIONS

- Mathematics
- 2003

In these lectures, we will talk about various aspects of the theory of fully nonlinear elliptic equations as they pertain to Global Differential Geometry. Advances in this theory in the last twenty…