Numerical criteria on the complex Hessian quotient equations with the Calabi symmetry
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908816901144576 |
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| author | Murakami, Rei |
| author_facet | Murakami, Rei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical criteria on the complex Hessian quotient equations with the Calabi symmetry Murakami, Rei Differential Geometry 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. |
| title | Numerical criteria on the complex Hessian quotient equations with the Calabi symmetry |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.03113 |