A Hilbert--Mumford criterion for generalised Monge--Ampère equations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915233928314880 |
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| author | Reboulet, Rémi |
| author_facet | Reboulet, Rémi |
| contents | We give a new numerical criterion in the spirit of GIT for existence of solutions to inverse Hessian equations, including in particular the J-equation. Our criterion is formulated in terms of stability of pairs in the sense of Paul. To that end, we build on previous work of the author with Dervan, and generalise a result of Zhang, proving isometry between generalised Chow line bundles and mixed Deligne pairings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hilbert--Mumford criterion for generalised Monge--Ampère equations Reboulet, Rémi Differential Geometry Algebraic Geometry We give a new numerical criterion in the spirit of GIT for existence of solutions to inverse Hessian equations, including in particular the J-equation. Our criterion is formulated in terms of stability of pairs in the sense of Paul. To that end, we build on previous work of the author with Dervan, and generalise a result of Zhang, proving isometry between generalised Chow line bundles and mixed Deligne pairings. |
| title | A Hilbert--Mumford criterion for generalised Monge--Ampère equations |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2504.06612 |