Embeddings and disjunction of Lagrangian pinwheels via rational blow-ups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913340204253184 |
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| author | Adaloglou, Nikolas |
| author_facet | Adaloglou, Nikolas |
| contents | We use the symplectic rational blow-up to study some Lagrangian pinwheels in symplectic rational manifolds. In particular, we determine which symplectic forms in the threefold blow-up of $\C P^2$ carry Lagrangian projective planes that can be made disjoint by a Hamiltonian isotopy. In addition, we show that such a disjunction is not possible in del Pezzo surfaces with Euler characteristic between $4$ and $7$. Finally, we determine which symplectic forms on $S^2\times S^2$ carry a Lagrangian $L_{3,1}$ pinwheel, answering a question of J. Evans. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Embeddings and disjunction of Lagrangian pinwheels via rational blow-ups Adaloglou, Nikolas Symplectic Geometry Algebraic Geometry Geometric Topology 53Dxx (Primary) 14J80 (Secondary) We use the symplectic rational blow-up to study some Lagrangian pinwheels in symplectic rational manifolds. In particular, we determine which symplectic forms in the threefold blow-up of $\C P^2$ carry Lagrangian projective planes that can be made disjoint by a Hamiltonian isotopy. In addition, we show that such a disjunction is not possible in del Pezzo surfaces with Euler characteristic between $4$ and $7$. Finally, we determine which symplectic forms on $S^2\times S^2$ carry a Lagrangian $L_{3,1}$ pinwheel, answering a question of J. Evans. |
| title | Embeddings and disjunction of Lagrangian pinwheels via rational blow-ups |
| topic | Symplectic Geometry Algebraic Geometry Geometric Topology 53Dxx (Primary) 14J80 (Secondary) |
| url | https://arxiv.org/abs/2405.02110 |