Numerical criteria on the complex Hessian quotient equations with the Calabi symmetry

Assuming Calabi symmetry, we prove that a numerical condition ensures the solvability of the complex Hessian quotient equation, as conjectured by Székelyhidi. We also propose a conjecture on the existence of a $k$-subharmonic representative in a given cohomology class and confirm it under the assumption of Calabi symmetry or when the class is semiample.

💡 Research Summary

The paper investigates the solvability of complex Hessian quotient equations on compact Kähler manifolds, focusing on the case where the underlying geometry enjoys Calabi symmetry. The equation under consideration is

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