Covariant symplectic geometry of binary forms and singularities of systems of rays (Q1308956)

The author generalizes the method for classifying the polynomial covariants of binary forms by using umbral calculus to obtain a general framework to describe the tensor invariants and the corresponding invariant subspaces of binary forms. As a consequence he obtains the unique invariant symplectic structure and Riemannian structure on the spaces of binary forms of odd and, respectively, even degree. In addition, the unique invariant contact structure on this space is found. Finally, by using the theory of common covariants of binary forms, the hierarchy of apolar coisotropic manifolds and generalized open swallowtails is derived.