Lagrangian skeleta, collars and duality
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917559787323392 |
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| author | Ballico, Edoardo Gasparim, Elizabeth Rubilar, Francisco Suzuki, Bruno |
| author_facet | Ballico, Edoardo Gasparim, Elizabeth Rubilar, Francisco Suzuki, Bruno |
| contents | We present a geometric realization of the duality between skeleta in $T^*\mathbb P^n$ and collars of local surfaces. Such duality is predicted by combining two auxiliary types of duality: on one side, symplectic duality between $T^*\mathbb P^n$ and a crepant resolution of the $A_n$ singularity; on the other side, toric duality between two types of isolated quotient singularities. We give a correspondence between Lagrangian submanifolds of the cotangent bundle and vector bundles on collars, and describe those birational transformations within the skeleton which are dual to deformations of vector bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_09540 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Lagrangian skeleta, collars and duality Ballico, Edoardo Gasparim, Elizabeth Rubilar, Francisco Suzuki, Bruno Symplectic Geometry Algebraic Geometry 53D05, 14D20 We present a geometric realization of the duality between skeleta in $T^*\mathbb P^n$ and collars of local surfaces. Such duality is predicted by combining two auxiliary types of duality: on one side, symplectic duality between $T^*\mathbb P^n$ and a crepant resolution of the $A_n$ singularity; on the other side, toric duality between two types of isolated quotient singularities. We give a correspondence between Lagrangian submanifolds of the cotangent bundle and vector bundles on collars, and describe those birational transformations within the skeleton which are dual to deformations of vector bundles. |
| title | Lagrangian skeleta, collars and duality |
| topic | Symplectic Geometry Algebraic Geometry 53D05, 14D20 |
| url | https://arxiv.org/abs/2112.09540 |