Poisson structures on the conifold and local Calabi-Yau threefolds
Edoardo Ballico, Elizabeth Gasparim, Thomas K\"oppe, Bruno Suzuki

TL;DR
This paper explores Poisson structures on local Calabi-Yau threefolds, especially focusing on the conifold, by classifying all possible holomorphic Poisson structures and describing bivector fields.
Contribution
It provides a complete classification of holomorphic Poisson structures on the conifold and describes bivector fields on local Calabi-Yau threefolds.
Findings
All possible holomorphic Poisson structures on the conifold are calculated.
Bivector fields on local Calabi-Yau threefolds are explicitly described.
The structure of Poisson brackets on these geometries is characterized.
Abstract
We describe bivector fields and Poisson structures on local Calabi-Yau threefolds which are total spaces of vector bundles on a contractible rational curve. In particular, we calculate all possible holomorphic Poisson structures on the conifold.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry
