Classification of Hamiltonian $S^1$-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910309962219520 |
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| author | Godinho, Leonor Mwakyoma-Oliveira, Grace T. Sepe, Daniele |
| author_facet | Godinho, Leonor Mwakyoma-Oliveira, Grace T. Sepe, Daniele |
| contents | In this paper, we classify Hamiltonian $S^1$-actions on compact, four dimensional symplectic orbifolds that have isolated singular points with cyclic orbifold structure groups, thus extending the classification due to Karshon to the orbifold setting. To such a space, we associated a combinatorial invariant, a labeled multigraph, that determines the isomorphism type of the space. Moreover, we show that any such space can be obtained by applying finitely many equivariant weighted blow-ups to a minimal space, i.e., one on which no equivariant weighted blow-down can be applied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of Hamiltonian $S^1$-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four Godinho, Leonor Mwakyoma-Oliveira, Grace T. Sepe, Daniele Symplectic Geometry 53D20, 53D35 In this paper, we classify Hamiltonian $S^1$-actions on compact, four dimensional symplectic orbifolds that have isolated singular points with cyclic orbifold structure groups, thus extending the classification due to Karshon to the orbifold setting. To such a space, we associated a combinatorial invariant, a labeled multigraph, that determines the isomorphism type of the space. Moreover, we show that any such space can be obtained by applying finitely many equivariant weighted blow-ups to a minimal space, i.e., one on which no equivariant weighted blow-down can be applied. |
| title | Classification of Hamiltonian $S^1$-actions on compact symplectic orbifolds with isolated cyclic singular points in dimension four |
| topic | Symplectic Geometry 53D20, 53D35 |
| url | https://arxiv.org/abs/2401.15466 |