  The purpose of this note is to show that W3 algebras originate from an
unusual interplay between the breakings of the reparametrization invariance
under the diffemorphism action on the cotangent bundle of a Riemann surface. It
is recalled how a set of smooth changes of local complex coordinates on the
base space are collectively related to a background within a symplectic
framework. The power of the method allows to calculate explicitly some primary
fields whose OPEs generate the algebra as explicit functions in the
coordinates: this is achieved only if well defined conditions are satisfied,
and new symmetries emerge from the construction. Moreoverer, when primary
flelds are introduced outside of a coordinate description the W3 symmetry
byproducts acquire a good geometrical definition with respect to holomorphic
changes of charts.
