On the universality of Baum-Fulton-MacPherson's Riemann-Roch for singular varieties
Let \(K_ 0(X)\) be the Grothendieck group of coherent algebraic sheaves on a variety \(X\), \(H_{2*}(X,Q)\) be the even part of usual \(Q\)-homology of \(X\) and \(Td_ *\) be the natural transformation \(K_ 0\to H_{2*}(\;,Q)\) introduced in [\textit{P. Baum}, \textit{W. Fulton} and \textit{R. D. MacPherson}, Publ. Math. Inst. Hautes Étud. Sci. 45, 101-145 (1975; Zbl 0332.14003)]. The author proves universality of \(Td_ *\): any natural transformation \(K_ 0\to H_{2*}(\;,Q)\) has the form \(\sum r_ i Td_{* i}\) for some rational numbers \(r_ i\), where \(Td_{* i}\) is the projection of \(Td_ *\) to the \(2i\)-dimensional component. The question on universality of the transformation \(c_ *\) of \textit{R. D. MacPherson} [Ann. Math., II. Ser. 100, 423-432 (1974; Zbl 0311.14001)] is discussed. Possibility of some extension of the transformation \(Td_ *\) is announced.
scientific article; zbMATH DE number 97943