Related papers: Chern classes of Schubert cells and varieties

We study a K-theoretic characteristic class of singular varieties, namely the equivariant motivic Chern class. We prove that the motivic Chern class is characterized by an axiom system inspired by that of "K-theoretic stable envelopes,"…

We prove a formula for the degrees of Ikeda and Naruse's $P$-Grothendieck polynomials using combinatorics of shifted tableaux. We show this formula can be used in conjunction with results of Hamaker, Marberg, and Pawlowski to obtain an…

Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a "Giambelli formula" expressing…

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…

Here, we utilize facts about the big Chern classes discovered by M. Kapranov and independently by M. V. Nori to prove certain results about the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0. In…

We give a characteristic-free proof that general codimension-1 Schubert varieties meet transversally in a Grassmannian and in some related varieties. Thus the corresponding intersection numbers computed in the Chow (and quantum Chow) rings…

We introduce immanant varieties, associated to simple characters of a finite group. They include well-studied classes of varieties, as Segre embeddings, Grassmannians and certain other classes of Chow varieties. For a one-dimensional…

The Dwyer-Fried invariants of a finite cell complex X are the subsets \Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,\Q) which parametrize the regular \Z^r-covers of X having finite Betti numbers up to degree i. In previous work, we…

Since Chern and Grothendieck, Chern's characteristic class theory has made significant progress. In particular with regard to the classes of singular varieties. Conjectured by Grothendieck and Deligne and demonstrated by MacPherson, Chern…

We give two formulas for the Chern-Schwartz-MacPherson class of symmetric and skew-symmetric degeneracy loci. We apply them in enumerative geometry, explore their algebraic combinatorics, and discuss K theory generalizations.

In this paper, I construct Chern classes in the rigid cohomology of P. Berthelot. We start by constructing Chern classes for proper varieties. To prove all the properties we have to reinterpret the construction in a crystalline way. Then we…

In this paper, we study the multi-rigidity problem in rational homogeneous spaces. A Schubert class is called multi-rigid if every multiple of it can only be represented by a union of Schubert varieties. We prove the multi-rigidity of…

We calculate the equivariant motivic Chern class for configuration space of a quasiprojective (maybe singular) variety and the space of vectors with different directions. We prove the formulas for generating series of these classes. We…

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 observe that linear relations among Chern-Mather classes of projective varieties are preserved by projective duality. We deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect…

Let $X$ be a complex nonsingular variety with globally generated tangent bundle. We prove that the signed Segre-MacPherson (SM) class of a constructible function on $X$ with effective characteristic cycle is effective. This observation has…

Let $X$ be a nonsingular complex variety and $D$ a reduced effective divisor in $X$. In this paper we study the conditions under which the formula $c_{SM}(1_U)=c(\textup{Der}_X(-\log D))\cap [X]$ is true. We prove that this formula is…

Let X be a symplectic or odd orthogonal Grassmannian which parametrizes isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove quantum Giambelli formulas which express an arbitrary Schubert class…

Let X=G/P be cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) We say a Schubert class [S] is Schur rigid if the only irreducible subvarieties Y of X with homology class…

Let $M(d,\chi)$ be the moduli space of semistable sheaves of rank 0, Euler characteristic $\chi$ and first Chern class $dH (d>0)$, with $H$ the hyperplane class in $\mathbb{P}^2$. We give a description of $M(d,\chi)$, viewing each sheaf as…