The mod-p cohomology ring of the extraspecial p-group of exponent p is studied for odd p. We investigate the subquotient ch(G) generated by Chern classes modulo the nilradical. The subring of ch(G) generated by Chern classes of one-dimensional representations was studied by Tezuka and Yagita

We prove a formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology Chern class of singular varieties, introduced by W. Fulton; and we discuss the relation between these classes and others, such as Mather

Abstract. We generalize the Chern class relation for the transversal intersec-tion of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. The relation is shown to hold for both the Chern– Schwartz–MacPherson class and the Chern–Fulton class

For a morphism f: X → Y with Y being nonsingular, the Ginzburg-Chern class of a constructible function α on the source variety X is defined to be the Chern-Schwartz-MacPherson class of the constructible function α followed by capping with the pull-back of the Segre class of the target variety Y

differentials be isomorphisms. We also consider the effect of splayedness on the Chern classes of sheaves of differential forms with logarithmic poles along splayed divisors, as well as on the Chern-Schwartz-MacPherson classes of the complements of these divisors. A postulated relation between these different

The bivariant theory was introduced by W. Fulton and R. MacPherson to unify both covariant and contravariant theories. They posed the problem of unique existence of a bivariant Chern class, i.e., a Grothendieck transformation from the bivariant theory F of constructible functions to the bivariant

Abstract. We extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the standard argument for the nonsingular case, involving

Abstract. We show how Chern clases of a Calabi Yau hypersurface in a toric Fano manifold can be expressed in terms of the holomorphic at a maximal degeneracy point period of its mirror. We also consider the relation between the Chern classes and the periods of mirrors for complete intersections

In this note we give a simple, model-independent construction of Chern classes as natural transformations from differential complex K-theory to differential integral cohomology. We verify the expected behaviour of these Chern classes with respect

that the conventional Euler characteristic of a compact nonsingular complex variety is the degree of the total Chern class of its tangent bundle (Poincaré-