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arXiv · 2412.03113

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

Rei Murakami
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Abstract

Assuming Calabi symmetry, we prove that a numerical condition ensures the solvability of the complex Hessian quotient equation, as conjectured by Sz\'ekelyhidi. 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.

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Rei Murakami. 2024-12-04. Numerical criteria on the complex Hessian quotient equations with the Calabi symmetry. https://arxiv.org/abs/2412.03113

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