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Holomorphic Jacobi manifolds and holomorphic contact groupoids

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Abstract

This paper belongs to a series of works aiming at exploring generalized (complex) geometry in odd dimensions. Holomorphic Jacobi manifolds were introduced and studied by the authors in a separate paper as special cases of generalized contact bundles. In fact, generalized contact bundles are nothing but odd dimensional analogues of generalized complex manifolds. In the present paper, we solve the integration problem for holomorphic Jacobi manifolds by proving that they integrate to holomorphic contact groupoids. A crucial tool in our proof is what we call the homogenization scheme, which allows us to identify holomorphic Jacobi manifolds with homogeneous holomorphic Poisson manifolds and holomorphic contact groupoids with homogeneous complex symplectic groupoids.

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Acknowledgements

We thank Alfonso G. Tortorella for providing a proof of Proposition 2.7.5. We also thank Damien Broka, Mathieu Stiénon, and Ping Xu for useful discussions. L. V. is member of the GNSAGA, INdAM.

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Authors and Affiliations

  1. DipMat, Università degli Studi di Salerno, via Giovanni Paolo II no 123, 84084, Fisciano, SA, Italy

    Luca Vitagliano

  2. Department of Mathematics, Penn State University, University Park, State College, PA, 16802, USA

    Aïssa Wade

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  1. Luca Vitagliano
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  2. Aïssa Wade
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Correspondence to Luca Vitagliano.

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Vitagliano, L., Wade, A. Holomorphic Jacobi manifolds and holomorphic contact groupoids. Math. Z. 294, 1181–1225 (2020). https://doi.org/10.1007/s00209-019-02320-x

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