On a generalization of MacPherson's Chern homology class. II (Q1813965)

[For part I see ibid. 65, No. 7, 242-244 (1989; Zbl 0728.14015).] For a nonsingular variety \(X\), a characteristic class of \(X\) is defined to be that of its tangent bundle \(TX\). As for the case of singular varieties, there is at the moment no general notion available of characteristic classes, mainly because one cannot define the tangent bundle. For the Chern class and the Todd class, there are singular versions; namely, Deligne-Grothendieck-MacPherson's theory \(C_ *\) (abbr. \(DGM\)-theory) of Chern class [cf. \textit{R. D. MacPherson}, Ann. Math., II. Ser. 100, 423-432 (1974; Zbl 0311.14001)[ and Baum-Fulton- MacPherson's theory \(Td_ *\) (abbr. \(BFM\)-theory) of Todd class [\textit{P. Baum}, \textit{W. Fulton} and \textit{R. MacPherson}, Publ. Math., Inst. Hautes Étud. Sci. 45, 101-145 (1975; Zbl 0332.14003)]. The author extended in part I of this paper [loc. cit.] DGM-theory \(C_ *\) of (total) Chern class to a ``DGM-type'' theory \(C_{t*}\) of the Chern polynomial, which includes DGM-theory \(C_ *\) as a special case. In this note we give a characterization of ``DGM-type'' theories of characteristic classes under certain conditions.