  We will describe the appearance of specific algebraic KdV potentials as a
consequence of a requirement on a integro-differential expression. This
expression belongs to a class generated by means of Virasoro vector fields
acting on the KdV field. The ``almost'' rational KdV fields are described in
terms of a geometrical locus of complex points. A class of solutions of this
locus has recently appeared as a description of any conformal Verma module
without degeneration.
