A formula for Segre classes of singular projective varieties (Q1117986)

The Segre class of a singular projective variety X is that of the normal cone of the diagonal in the product \(X\times X\). This class was introduced by K. W. Johnson (and W. Fulton) [see \textit{K. W. Johnson}, Acta Math. 140, 49-74 (1978; Zbl 0373.14005)] to study immersions and embeddings. In the author's earlier work [Trans. Am. Math. Soc. 298, 169- 191 (1986; Zbl 0632.14019)], motivated by the remarkable relation between MacPherson's Chern class and Chern-Mather class (i.e., the Dubson formula) he related the Johnson's Segre class and the Segre-Mather class for hypersurfaces with codimension one singularities and \(X^ n\subset {\mathbb{P}}^{2n}\) with isolated singularities. In the present paper the author generalizes his earlier results to the case of \(X^ n\subset {\mathbb{P}}^ N\) with singularities of codimension N- n (N\(\leq 2n)\).