Poisson structures on the conifold and local Calabi-Yau threefolds

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.