The universal Poisson deformation of hypertoric varieties and some classification results

In this paper, we study and describe the universal Poisson deformation space of hypertoric varieties concretely. first application, show that affine as conical symplectic are classified by associated regular matroids (this is a partial generalization result Arbo Proudfoot). As corollary, obtain criterion when two quiver whose dimension vector have all coordinates equal to one isomorphic each other. Then 4- 6-dimensional give some examples 8-dimensional which cannot be raised such varieties. second compute explicitly number projective crepant resolutions 4-dimensional using combinatorics hyperplane arrangements.