Packing Integral Tori in Del Pezzo Surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910369839054848 |
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| author | Boustany, Karim |
| author_facet | Boustany, Karim |
| contents | We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in $\mathbb{S}^{2} \times \mathbb{S}^{2}$ to the Del Pezzo surfaces $(\mathbb{D}_{n}, ω_{\mathbb{D}_{n}})$ for $n = 1, \dots, 5$. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection $\{L_{i}\}$ of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collection must intersect at least one of the $L_{i}$. We show that one can always find such a packing consisting of only the Clifford torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09334 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Packing Integral Tori in Del Pezzo Surfaces Boustany, Karim Symplectic Geometry We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in $\mathbb{S}^{2} \times \mathbb{S}^{2}$ to the Del Pezzo surfaces $(\mathbb{D}_{n}, ω_{\mathbb{D}_{n}})$ for $n = 1, \dots, 5$. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection $\{L_{i}\}$ of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collection must intersect at least one of the $L_{i}$. We show that one can always find such a packing consisting of only the Clifford torus. |
| title | Packing Integral Tori in Del Pezzo Surfaces |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2308.09334 |