Brane quantization of toric Poisson varieties
In this paper we propose a noncommutative generalization of the relationship between compact Kähler manifolds and complex projective algebraic varieties. Beginning with a prequantized Kähler structure, we use a holomorphic Poisson tensor to deform the underlying complex structure into a generalized...
| Autori principali: | , |
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| Natura: | Journal article |
| Lingua: | English |
| Pubblicazione: |
Springer
2022
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| _version_ | 1826309395915472896 |
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| author | Bischoff, F Gualtieri, M |
| author_facet | Bischoff, F Gualtieri, M |
| author_sort | Bischoff, F |
| collection | OXFORD |
| description | In this paper we propose a noncommutative generalization of the relationship between compact Kähler manifolds and complex projective algebraic varieties. Beginning with a prequantized Kähler structure, we use a holomorphic Poisson tensor to deform the underlying complex structure into a generalized complex structure, such that the prequantum line bundle and its tensor powers deform to a sequence of generalized complex branes. Taking homomorphisms between the resulting branes, we obtain a noncommutative deformation of the homogeneous coordinate ring. As a proof of concept, this is implemented for all compact toric Kähler manifolds equipped with an R-matrix holomorphic Poisson structure, resulting in what could be called noncommutative toric varieties. To define the homomorphisms between generalized complex branes, we propose a method which involves lifting each pair of generalized complex branes to a single coisotropic A-brane in the real symplectic groupoid of the underlying Poisson structure, and compute morphisms in the A-model between the Lagrangian identity bisection and the lifted coisotropic brane. This is done with the use of a multiplicative holomorphic Lagrangian polarization of the groupoid. |
| first_indexed | 2024-03-07T07:33:34Z |
| format | Journal article |
| id | oxford-uuid:8b93325c-9ddb-4ff5-aa4a-0527da435dc7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:33:34Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:8b93325c-9ddb-4ff5-aa4a-0527da435dc72023-02-21T10:16:06ZBrane quantization of toric Poisson varietiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8b93325c-9ddb-4ff5-aa4a-0527da435dc7EnglishSymplectic ElementsSpringer2022Bischoff, FGualtieri, MIn this paper we propose a noncommutative generalization of the relationship between compact Kähler manifolds and complex projective algebraic varieties. Beginning with a prequantized Kähler structure, we use a holomorphic Poisson tensor to deform the underlying complex structure into a generalized complex structure, such that the prequantum line bundle and its tensor powers deform to a sequence of generalized complex branes. Taking homomorphisms between the resulting branes, we obtain a noncommutative deformation of the homogeneous coordinate ring. As a proof of concept, this is implemented for all compact toric Kähler manifolds equipped with an R-matrix holomorphic Poisson structure, resulting in what could be called noncommutative toric varieties. To define the homomorphisms between generalized complex branes, we propose a method which involves lifting each pair of generalized complex branes to a single coisotropic A-brane in the real symplectic groupoid of the underlying Poisson structure, and compute morphisms in the A-model between the Lagrangian identity bisection and the lifted coisotropic brane. This is done with the use of a multiplicative holomorphic Lagrangian polarization of the groupoid. |
| spellingShingle | Bischoff, F Gualtieri, M Brane quantization of toric Poisson varieties |
| title | Brane quantization of toric Poisson varieties |
| title_full | Brane quantization of toric Poisson varieties |
| title_fullStr | Brane quantization of toric Poisson varieties |
| title_full_unstemmed | Brane quantization of toric Poisson varieties |
| title_short | Brane quantization of toric Poisson varieties |
| title_sort | brane quantization of toric poisson varieties |
| work_keys_str_mv | AT bischofff branequantizationoftoricpoissonvarieties AT gualtierim branequantizationoftoricpoissonvarieties |