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Quasi-periodic solutions of the KP hierarchy acted by vertex operators arestudied. We show, with the aid of the Sato Grassmannian, that solutions thusconstructed correspond to torsion free rank one sheaves on some singularalgebraic curves whose normalizations are the non-singular curves correspondingto the seed quasi-periodic solutions. It means that the action of the vertexoperator has an effect of creating singular points on an algebraic curve. Wefurther check, by examples, that solutions obtained here can be considered assolitons on quasi-periodic backgrounds, where the soliton matrices aredeterimed by parameters in the vertex operators.

Vertex Operators of the KP hierarchy and Singular Algebraic Curves