Low-dimensional bihamiltonian structures of topological type

We construct local bihamiltonian structures from classical W-algebras associated with non-regular nilpotent elements of regular semisimple type in Lie algebras of types A2 and A3. They form exact Poisson pencils and admit a dispersionless limit, and their leading terms define logarithmic or trivial Dubrovin-Frobenius manifolds. We calculate the corresponding central invariants, which are expected to be constants. In particular, we get Dubrovin-Frobenius manifolds associated with the focused Schrödinger equation and Hurwitz space M0;1,0 and the corresponding bihamiltonian structures of topological type.