Poisson modules and generalized geometry

2009/05/20 by Nigel Hitchin, Hitchin, Nigel
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #msc:53C56 #msc:53D17

paper · pdf · doi:10.48550/arxiv.0905.3227

Dedicated to S-T Yau on the occasion of his 60th birthday

arxiv created 2009/05/20 · arxiv updated 2009/12/01

Abstract

The Serre construction of rank two holomorphic bundles with a section is adapted to construct generalized holomorphic bundles on a generalized complex 4-manifold from the data of a set of points on an elliptic curve. The motivation is the special case of rank two Poisson modules on a complex surface with a holomorphic Poisson structure.

Related

• Poisson geometry of parabolic bundles on Elliptic curves
• Poisson structures and birational morphisms associated with bundles on elliptic curves
• Singularities and Poisson geometry of certain representation spaces
• Holomorphic Poisson Cohomology
• Integration of the elliptic tangent bundle and elliptic Poisson structures