Related papers: Chern classes of splayed intersections
In this paper we compare different notions of transversality for possible singular complex algebraic or analytic subsets of an ambient complex manifold and prove a refined intersection formula for their Chern-Schwartz-MacPherson classes. In…
There is an explicit formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety (in characteristic $0$) in terms of the Segre class of its jacobian subscheme; this has been known for a number of years.…
We study intersection theory and Chern classes of reflexive sheaves on normal varieties. In particular, we define generalization of Mumford's intersection theory on normal surfaces to higher dimensions. We also define and study the second…
For a large class of possibly singular complete intersections we prove a formula for their Chern-Schwartz-MacPherson classes in terms of a single blowup along a scheme supported on the singular loci of such varieties. In the hypersurface…
The Chern-Fulton class is a generalization of Chern class to the realm of arbitrary embeddable schemes. While Chern-Fulton classes are sensitive to non-reduced scheme structure, they are not sensitive to possible singularities of the…
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…
We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a nonsingular variety M `interpolates' between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and…
We obtain several new characterizations of splayedness for divisors: a Leibniz property for ideals of singularity subschemes, the vanishing of a `splayedness' module, and the requirements that certain natural morphisms of modules and…
We generalize Fulton's Residual Intersection Theorem for the Segre class and express the Segre classes of schemes with regularly embedded components in terms of the Chern classes of the normal bundles to the components and their…
We consider two classical extensions for singular varieties of the usual Chern classes of complex manifolds, namely the total Schwartz-MacPherson and Fulton-Johnson classes, $c^{SM}(X)$ and $c^{FJ}(X)$. Their difference (up to sign) is the…
A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety which have almost all the properties of the…
We introduce a class extending the notion of Chern-Mather class to possibly nonreduced schemes, and use it to express the difference between Schwartz-MacPherson's Chern class and the class of the virtual tangent bundle of a singular…
We study the behavior of the Chern classes of graph hypersurfaces under the operation of deletion-contraction of an edge of the corresponding graph. We obtain an explicit formula when the edge satisfies two technical conditions, and prove…
The existence of bivariant Chern classes was conjectured by W.Fulton and R.MacPherson and proved by J.P.Brasselet for cellular morphisms of analytic varieties. In this paper we show that restricted to morphisms whose target varieties are…
Motivic integration and MacPherson's transformation are combined in this paper to construct a theory of "stringy" Chern classes for singular varieties. These classes enjoy strong birational invariance properties, and their definition…
The Chern class of the sheaf of logarithmic derivations along a simple normal crossing divisor equals the Chern-Schwartz-MacPherson class of the complement of the divisor. We extend this equality to more general divisors, which are locally…
We give a general formula for the defect appearing in the Verdier-type Riemann-Roch formula for Chern-Schwartz-MacPherson classes in the case of a regular embedding. Our proof of this formula uses the constructible function version of…
We give explicit formulas for the Chern-Schwartz-MacPherson classes of all Schubert varieties in the Grassmannian of $d$-planes in a vector space, and conjecture that these classes are effective. We prove this is the case for (very) small…
We define an `enriched' notion of Chow groups for algebraic varieties, agreeing with the conventional notion for complete varieties, but enjoying a functorial push-forward for arbitrary maps. This tool allows us to glue…
Let $V$ be a possibly singular scheme-theoretic complete intersection subscheme of $\mathbb{P}^n$ over an algebraically closed field of characteristic zero. Using a recent result of Fullwood ("On Milnor classes via invariants of singular…