The Local Product Theorem for bihamiltonian structures
  In this work one proves that, around each point of a dense open set (regular points), a real analytic or holomorphic bihamiltonian structure decomposes into a product of a Kronecker bihamiltonian structure and a symplectic one if a necessary condition on the characteristic polynomial of the symplectic factor holds. Moreover we give an example of bihamiltonian structure for showing that this result does not extend to the $C^\infty$-category.   Thus a classical problem on the geometric theory of bihamiltonian structures is solved at almost every point. 
Francisco-Javier Turiel
math.SG math.DG