Branes on Poisson varieties

Details Branes on Poisson varieties Branes on Poisson varieties

2007-10-15

arxiv.org/abs/0710.2719v2

Mathematics

Differential Geometry

Dedicated to Nigel Hitchin on the occasion of his sixtieth birthday. Corrected several errors and added references

Scientific paper

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.

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