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We establish a general computational scheme designed for a systematiccomputation of characteristic classes of singular complex algebraic varietiesthat satisfy a Gysin axiom in a transverse setup. This scheme is explicitlygeometric and of a recursive nature terminating on genera of explicitcharacteristic subvarieties that we construct. It enables us e.g. to applyintersection theory of Schubert varieties to obtain a uniqueness result forsuch characteristic classes in the homology of an ambient Grassmannian. Ourframework applies in particular to the Goresky-MacPherson L-class by virtue ofthe Gysin restriction formula obtained by the first author in previous work. Weillustrate our approach for a systematic computation of the L-class in terms ofnormally nonsingular expansions in examples of singular Schubert varieties thatdo not satisfy Poincar\'{e} duality over the rationals.

The Uniqueness Theorem for Gysin Coherent Characteristic Classes of Singular Spaces