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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2017 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862732083425705984 |
|---|---|
| author | Caine, A. Givens, B.N. |
| author_facet | Caine, A. Givens, B.N. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T19:30:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148600 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:30:06Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Caine, A. Givens, B.N. 2019-02-18T16:28:14Z 2019-02-18T16:28:14Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148600 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. Portions of this work were completed independently by the two authors during independent
 sabbatical leaves from California State Polytechnic University Pomona and, separately, while
 supported by the Provost’s Teacher-Scholar Program. We appreciate this support and the
 suggestions from the referees which improved the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Toric Poisson Structures of Type (1,1) and their Cohomology Article published earlier |
| spellingShingle | On Toric Poisson Structures of Type (1,1) and their Cohomology Caine, A. Givens, B.N. |
| title | 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_short | On Toric Poisson Structures of Type (1,1) and their Cohomology |
| title_sort | on toric poisson structures of type (1,1) and their cohomology |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148600 |
| work_keys_str_mv | AT cainea ontoricpoissonstructuresoftype11andtheircohomology AT givensbn ontoricpoissonstructuresoftype11andtheircohomology |