Related papers: Bruhat strata and F-zips with additional structure…

In order to establish Fredholm theory on stratified topological Banach manifolds in Gromov-Witten theory, we have introduced flat structures on such manifolds in [L4]. Such a structure is obtained from local flat coordinate charts. The…

Let $\mathcal{G}$ be a connected reductive almost simple group over the Witt ring $W(\mathbb{F})$ for $\mathbb{F}$ a finite field of characteristic $p$. Let $R$ and $R'$ be complete noetherian local $W(\mathbb{F})$ -algebras with residue…

Quasi-homogeneous surfaces, or Gizatullin surfaces, are normal affine surfaces such that there exists an open orbit of the automorphism group with a finite complement. If the action of the automorphism group is transitive, the surface is…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

We prove a result that relates the number of homomorphisms from the fundamental group of a compact nonorientable surface to a finite group $G$, where conjugacy classes of the boundary components of the surface must map to prescribed…

The totally nonnegative part of a partial flag variety G/P is known to have a decomposition into semi-algebraic cells. We show that the closure of a cell is again a union of cells and give a combinatorial description of the closure…

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, $\xi \colon P \to \Sigma$ a principal $G$-bundle, let $N(\xi)$ denote the moduli space of central Yang-Mills connections on $\xi$, for suitably chosen…

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal…

Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…

We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e. partial flag varieties associated to maximal parabolic subgroups in a simple algebraic group. We explain how the…

We begin with a comprehensive discussion of the punctual Hilbert scheme of the regular two-dimensional local ring in terms of the Gr\"obner cells. These schemes are the most degenerate fibers of the Grothendieck-Deligne norm map (the…

We consider real forms of relatively minimal rational surfaces F_m. Connected components of moduli of real non-singular curves in |-2K_{F_m}| had been classified recently for m=0, 1, 4 in math.AG/0312396. Applying similar methods, here we…

Given a del Pezzo surface of degree d between 1 and 6, possibly with rational double points, we construct a "tautological" holomorphic G-bundle over X, where G is a reductive group which is an appropriate conformal form of the simply…

Let $G$ be a simple algebraic group over an algebraically closed field $k$. Let $\Gamma$ be a finite group acting on $G$. We classify and compute the local types of $(\Gamma, G)$-bundles on a smooth projective $\Gamma$-curve in terms of the…

Given a split $\mathbb{P}$-functor $F:\mathcal{D}^b(X) \to \mathcal{D}^b(Y)$ between smooth projective varieties, we provide necessary and sufficient conditions, in terms of the Hochschild cohomology of $X$, for it to become spherical on…

Let a split element of a connected semisimple Lie group act on one of its flag manifolds. We prove that each connected set of fixed points of this action is itself a flag manifold. With this we can obtain the generalized Bruhat…

While the intersection of the Grassmannian Bruhat decompositions for all coordinate flags is an intractable mess, the intersection of only the cyclic shifts of one Bruhat decomposition turns out to have many of the good properties of the…

We address a conjecture (referred to as sur in the literature) in the representation theory of a reductive p-adic Lie group G which has important implications for the relationship between mod-p smooth representations and pro-p Iwahori-Hecke…

We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme…