Related papers: Hessenberg varieties associated to ad-nilpotent id…

The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety's cohomology ring carries a symmetric group action, and he offered a deep geometric construction of this action.…

A key tool for the study of an affine Hecke algebra $\mathcal{H}$ is provided by Springer theory of the Langlands dual group via the realization of $\mathcal{H}$ as equivariant $K$-theory of the Steinberg variety. We prove a similar…

We prove a conjecture by Lusztig, which describes the tensor categories of perverse sheaves on affine flag manifolds, with tensor structure provided by truncated convolution, in terms of the Langlands dual group. We also give a geometric…

We prove a fibration property for varieties with Hilbert-type properties and give applications to rational points on varieties with nef tangent bundle.

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

We introduce parabolic multiplicative affine Springer fibers, which resemble the admissible union of affine Deligne Lusztig varieties in the affine flag variety. We also study their global counterparts called parabolic multiplicative…

In this paper, we study the subvarieties of a complex flag variety that are invariant under the action of a maximal torus. Using combinatorial techniques derived from matroid theory, we introduce a decomposition of this variety into affine,…

In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all Poincar\'e duals of smaller regular nilpotent Hessenberg subvarieties. In particular, all of…

We show that Lang's hyperbolic and function version conjectures hold for surfaces $S$ of general type having a fibration of general type onto a curve $C$. The notion of multiplicity used is natural, but not classical, which leds to orbifold…

Let G be a simply-connected simple compact Lie group over the complex numbers. The affine Grassmannian is a projective ind-variety, homotopy-equivalent to the loop space of G and closely analogous to a maximal flag variety of the classical…

We prove in type A a conjecture which describes the ideal of transversal slices to spherical Schubert varieties in the affine Grassmannian. As a corollary, we prove a modular description (due to Finkelberg-Mirkovi\'c) of the spherical…

We discuss some connections between the closure $\bar F$ of a Steinberg fiber in the wonderful compactification of an adjoint group and the affine Deligne-Lusztig varieties $X_w(1)$ in the affine flag variety. Among other things, we…

According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformations $f_{n}:\overline{\mathcal{P}}_{n}\to \mathcal{B}_{n}$ of…

In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail…

We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A,…

We establish several foundational results regarding the Grothendieck-Springer affine fibration. More precisely, we prove some constructibility results on the affine Grothendieck-Springer sheaf and its coinvariants, enrich it with a group of…

An affine Hecke algebras can be realized as an equivariant K-group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the…

Hessenberg varieties $\mathcal{H}(X,H)$ form a class of subvarieties of the flag variety $G/B$, parameterized by an operator $X$ and certain subspaces $H$ of the Lie algebra of $G$. We identify several families of Hessenberg varieties in…

We prove a boundedness-theorem for families of abelian varieties with real multiplication. More generally, we study curves in Hilbert modular varieties from the point of view of the Green Griffiths-Lang conjecture claiming that entire…

We identify, up to homeomorphisms, the affine Springer fibers for GL(n) on a local field of equal characteristics with some coverings of compactified jacobians of singular projective curves. This allows us to prove an irreducibility…