Chern classes and generators

Chow Homology and Chern Classes

Stringy Chern classes

Work of Dixon, Harvey, Vafa and Witten in the 80’s ([DHVW85]) introduced a notion of Euler characteristic (for quotients of a torus by a finite group) which became known as the physicist’s orbifold Euler number. In the 90’s V. Batyrev introduced a notion of stringy Euler number ([Bat99b]) for ‘arbitrary Kawamata log-terminal pairs’, proving that this number agrees with the physicist’s orbifold ...

Chern Classes for Singular Hypersurfaces

We prove a simple formula for MacPherson’s Chern class of hypersurfaces in nonsingular varieties. The result highlights the relation between MacPherson’s class and other definitions of homology Chern classes of singular varieties, such as Mather’s Chern class and the class introduced by W. Fulton in [Fulton], 4.2.6. §0. Introduction 2 §1. Statements of the result 4 §1.1. MacPherson’s Chern clas...

Chern Classes of Splayed Intersections

We generalize the Chern class relation for the transversal intersection 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. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation unde...

Foliations with vanishing Chern classes

In this paper we aim at the description of foliations having tangent sheaf TF with c1(TF) = c2(TF) = 0 on non-uniruled projective manifolds. We prove that the universal covering of the ambient manifold splits as a product, and that the Zariski closure of a general leaf of F is an Abelian variety. It turns out that the analytic type of the Zariski closures of leaves may vary from leaf to leaf. W...