An elementary approach to the polynomial tau-functions of the KP hierarchy

We give an elementary construction of the solutions of the KP hierarchy ass ociated with polynomial tau-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a co nsequence, we establish a Wronskian formula for the polynomial tau-function s of the KP hierarchy. This formula, known in the literature, is obtained v ery directly.