Poisson Traces and D-Modules on Poisson Varieties
نویسندگان
چکیده
منابع مشابه
Poisson traces, D-modules, and symplectic resolutions
We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a ...
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We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kähler 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 Kähler structures, and u...
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We compute the space of Poisson traces on symmetric powers of affine symplectic varieties. In the case of symplectic vector spaces, we also consider the quotient by the diagonal translation action, which includes the quotient singularities T C/Sn associated to the type A Weyl group Sn and its reflection representation C . We also compute the full structure of the natural D-module, previously de...
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Generalized complex structures were introduced as a common format for discussing both symplectic and complex manifolds, but the most interesting examples are hybrid objects – part symplectic and part complex. One such class of examples consists of holomorphic Poisson surfaces, but in [5],[6] Cavalcanti and Gualtieri also construct generalized complex 4-manifolds with similar features which are ...
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We prove a result that can be applied to determine the finitedimensional simple Poisson modules over a Poisson algebra and apply it to numerous examples. In the discussion of the examples, the emphasis is on the correspondence with the finite-dimensional simple modules over deformations and on the behaviour of finite-dimensional simple Poisson modules on the passage from a Poisson algebra to th...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2010
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-010-0085-4