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Mathematics > Differential Geometry

arXiv:0710.2719 (math)
[Submitted on 15 Oct 2007 (v1), last revised 20 Jul 2010 (this version, v2)]

Title:Branes on Poisson varieties

Authors:Marco Gualtieri
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Abstract:We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of isomorphism between holomorphic Poisson manifolds, which is non-holomorphic in nature. Finally we show an equivalence between certain configurations of branes on Poisson varieties and generalized Kaehler structures, and use this to construct explicitly new families of generalized Kaehler structures on compact holomorphic Poisson manifolds equipped with positive Poisson line bundles (e.g. Fano manifolds). We end with some speculations concerning the connection to non-commutative algebraic geometry.
Comments: Dedicated to Nigel Hitchin on the occasion of his sixtieth birthday. Corrected several errors and added references
Subjects: Differential Geometry (math.DG); High Energy Physics - Theory (hep-th); Symplectic Geometry (math.SG)
MSC classes: 53C15, 53C80, 53D17
Cite as: arXiv:0710.2719 [math.DG]
  (or arXiv:0710.2719v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.2719

Submission history

From: Marco Gualtieri [view email]
[v1] Mon, 15 Oct 2007 06:21:33 UTC (24 KB)
[v2] Tue, 20 Jul 2010 19:31:23 UTC (31 KB)
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