On Toric Poisson Structures of Type (1,1) and their Cohomology
We classify real Poisson structures on complex toric manifolds of type (1,1) and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in each of the distinguished holomorphic coordinate charts deter...
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| Дата: | 2017 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148600 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Toric Poisson Structures of Type (1,1) and their Cohomology / A. Caine, B.N. Givens // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 8 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1486002019-02-19T01:28:36Z On Toric Poisson Structures of Type (1,1) and their Cohomology Caine, A. Givens, B.N. We classify real Poisson structures on complex toric manifolds of type (1,1) and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in each of the distinguished holomorphic coordinate charts determined by the open cones of the associated simplicial fan. As an approximation to the smooth cohomology problem in each Cn chart, we consider the Poisson differential on the complex of polynomial multi-vector fields. For the algebraic problem, we compute H⁰ and H¹ under the assumption that the Poisson structure is generically non-degenerate. The paper concludes with numerical investigations of the higher degree cohomology groups of (C²,πB) for various B. 2017 Article On Toric Poisson Structures of Type (1,1) and their Cohomology / A. Caine, B.N. Givens // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D17; 37J15 DOI:10.3842/SIGMA.2017.023 http://dspace.nbuv.gov.ua/handle/123456789/148600 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We classify real Poisson structures on complex toric manifolds of type (1,1) and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in each of the distinguished holomorphic coordinate charts determined by the open cones of the associated simplicial fan. As an approximation to the smooth cohomology problem in each Cn chart, we consider the Poisson differential on the complex of polynomial multi-vector fields. For the algebraic problem, we compute H⁰ and H¹ under the assumption that the Poisson structure is generically non-degenerate. The paper concludes with numerical investigations of the higher degree cohomology groups of (C²,πB) for various B. |
| format |
Article |
| author |
Caine, A. Givens, B.N. |
| spellingShingle |
Caine, A. Givens, B.N. On Toric Poisson Structures of Type (1,1) and their Cohomology Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Caine, A. Givens, B.N. |
| author_sort |
Caine, A. |
| title |
On Toric Poisson Structures of Type (1,1) and their Cohomology |
| title_short |
On Toric Poisson Structures of Type (1,1) and their Cohomology |
| title_full |
On Toric Poisson Structures of Type (1,1) and their Cohomology |
| title_fullStr |
On Toric Poisson Structures of Type (1,1) and their Cohomology |
| title_full_unstemmed |
On Toric Poisson Structures of Type (1,1) and their Cohomology |
| title_sort |
on toric poisson structures of type (1,1) and their cohomology |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148600 |
| citation_txt |
On Toric Poisson Structures of Type (1,1) and their Cohomology / A. Caine, B.N. Givens // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 8 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT cainea ontoricpoissonstructuresoftype11andtheircohomology AT givensbn ontoricpoissonstructuresoftype11andtheircohomology |
| first_indexed |
2023-05-20T17:30:13Z |
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2023-05-20T17:30:13Z |
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1796153441060388864 |