On Toric Poisson Structures of Type (1,1) and their Cohomology
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On Toric Poisson Structures of Type (1,1) and their Cohomology
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| Creator |
Caine, A.
Givens, B.N. |
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| 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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| Date |
2019-02-18T16:28:14Z
2019-02-18T16:28:14Z 2017 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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