Branes on Poisson varieties

By M. Gualtieri. 2007

154 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d6a050d986217f03842c1e261fb8d54290a73bcd

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Citations in the corpus

Background independent action for double field theory (2010, background): “One geometry has been proposed in this context by Siegel [5], and generalised geometry [7, 8, 9, 10, 11] might provide”
Generalized Kähler Geometry (2010, methodology): “Hence we obtain a Morita equivalence between holomorphic Poisson structures, generalizing the result in [24] on Morita equivalence for a specific construction of generalized Kähler structures.”
Lectures on generalized geometry (2010, unknown): “we shall see in the next lecture, the Kodaira-Spencer class is zero. This is consistent with some concrete constructions of one-parameter families of bihermitian metrics on Fano manifolds in [14] and [7], where I+(t) and I−(t) are all equivalent under a diﬀeomorphism. One corollary of Goto’s theorem”
Branes and Quantization (2008, background): “and made more precise in [9, 10 ], partly in the framework of generalized complex geometry”
On the Riemann tensor in double field theory (2011, background): “Finally, generalized geometry [27] also features closely related connections and curvatures; see [26] for a recent concise exposition.”
Spheres, Generalised Parallelisability and Consistent Truncations (2014, background): “A generalised connection[15,23,66] is a first-order linear differential operator DM which acts on generalised vectors as DMV = ∂MV + N M PV P .”
The spacetime of double field theory: Review, remarks, and outlook (2013, methodology): “In this case DFT may be viewed as the physical implementation of the ‘generalized geometry’ program of HitchinGualtieri [15–17].”
T-duality, generalized geometry and non-geometric backgrounds (2008, background): “[33] this has given us a split of the generalized tangent space E = C0 + C ⊥ 0 spanned by Ea and Ea respectively.”
Doubled α′-geometry (2013, unknown): “27 5.2 Projection to divergence free tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30”