Chern Classes of Splayed Intersections
نویسندگان
چکیده
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 under the assumption that one of the varieties is a general very ample divisor.
منابع مشابه
Splayed divisors and their Chern classes
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 sheaves of logarithmic derivations and logarithmic differentials be isomorphisms. We also consider the effect of splayedness on the Chern classes of sheaves of dif...
متن کاملHirzebruch-milnor Classes of Complete Intersections
We prove a new formula for the Hirzebruch-Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the Chern-Milnor classes in the hypersurface case that was conjectured by S. Yokura and was proved by A. Parusinski and P. Pragacz. It also generalizes a formula of J. ...
متن کامل2 00 5 Chern classes of reductive groups and an adjunction formula Valentina
In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete intersections in reductive groups. In the case where the complete intersection is a curve, this formula gives an explicit answer for the Euler characteristi...
متن کاملChern classes of compactifications of reductive groups
In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. Then “Chern classes” of the tangent bundle are used to carry over to the case of an arbitrary reductive group some of the well-known results that hold for a complex torus. One of the results of this paper is a formula for the Chern classes of all regular equivariant co...
متن کاملResidual intersection theory with reducible schemes
We develop a formula (Theorem 5.1) which allows to compute top Chern classes of vector bundles on the vanishing locus V (s) of a section of this bundle. This formula particularly applies in the case when V (s) is the union of locally complete intersections giving the individual contribution of each component and their mutual intersections. We conclude with applications to the enumeration of rat...
متن کامل