Related papers: Chern-Mather classes of toric varieties

We introduce a certain index of a collection of germs of 1-forms on a germ of a singular variety which is a generalization of the local Euler obstruction corresponding to Chern numbers different from the top one.

We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and simply connected compact Lie groups and…

We prove a Kotake-Narasimhan type theorem in general ultradifferentiable classes given by weight matrices. In doing so we simultaneously recover and partially generalize the known results for classes given by weight sequences and weight…

In this paper we consider the real topological K-groups of a toric manifold M, which turns out to be closely related to the topology of the small cover MR, the fixed points under the canonical conjugation on M . Following the work of Bahri…

We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely…

In this paper, we introduce the notion of "extension" of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or…

We generalize the K\"unneth formula for Chow groups to an arbitrary OBM-homology theory satisfying descent (e.g. algebraic cobordism) when taking a product with a toric variety. As a corollary we obtain a universal coefficient theorem for…

A particular case of Bergeron-Venkatesh's conjecture predicts that torsion classes in the cohomology of Shimura varieties are rather rare. According to this and for Kottwitz-Harris-Taylor type of Shimura varieties, we first associate to…

We write the equivariant Todd class of a general complete toric variety as an explicit combination of the orbit closures, the coefficients being analytic functions on the Lie algebra of the torus which satisfy Danilov's requirement.

We generalize the author's formula for Gromov-Witten invariants of symplectic toric manifolds (see math.AG/0006156) to those needed to compute the quantum product of more than two classes directly, i.e. involving the pull-back of the…

This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…

This is a note on MacPherson's Chern class for algebraic stacks, based on a previous paper of the author [arXiv:math/0407348]. We also discuss other additive characteristic classes in the same manner.

Let M be a smooth complex projective variety, bearing a K\"ahler symplectic form \omega and a Hamiltonian action of a torus T, with finitely many fixed points M^T. One standard form of the Duistermaat-Heckman theorem gives a formula for M's…

For a complete toric variety, we obtain an explicit formula for the localized equivariant Todd class in terms of the combinatorial data -- the fan. This is based on the equivariant Riemann-Roch theorem and the computation of the equivariant…

Motivic Chern and Hirzebruch classes are polynomials with K-theory and homology classes as coefficients, which specialize to Chern-Schwartz-MacPherson classes, K-theory classes, and Cappell-Shaneson L-classes. We provide formulas to compute…

Using raising operators and geometric arguments, we establish formulas for the K-theory classes of degeneracy loci in classical types. We also find new determinantal and Pfaffian expressions for classical cases considered by Giambelli: the…

Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This…

Michael Gromov has recently initiated what he calls ``symbolic algebraic geometry", in which objects are proalgebraic varieties: a proalgebraic variety is by definition the projective limit of a projective system of algebraic varieties. In…

Lop\'ez de Medrano-Rin\'con-Shaw defined Chern-Schwartz-MacPherson cycles for an arbitrary matroid $M$ and proved by an inductive geometric argument that the unsigned degrees of these cycles agree with the coefficients of $T(M;x,0)$, where…

We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on complete toric…