On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912383086100480 |
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| author | Kessler, Liat Wardenski, Nikolas |
| author_facet | Kessler, Liat Wardenski, Nikolas |
| contents | Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The additional assumptions allow us to use results proven by $J$-holomorphic methods. Gonzales' answer was applied by Cho in proving that if the underlying symplectic manifold is positive monotone then the space is isomorphic to a Fano manifold with a holomorphic $S^1$-action. We show that our variation is enough for Cho's application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data Kessler, Liat Wardenski, Nikolas Symplectic Geometry 53D35 Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The additional assumptions allow us to use results proven by $J$-holomorphic methods. Gonzales' answer was applied by Cho in proving that if the underlying symplectic manifold is positive monotone then the space is isomorphic to a Fano manifold with a holomorphic $S^1$-action. We show that our variation is enough for Cho's application. |
| title | On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data |
| topic | Symplectic Geometry 53D35 |
| url | https://arxiv.org/abs/2505.14000 |