Related papers: Drinfeld Moduli Schemes and Infinite Grassmannians
This is a survey article on moduli of affine schemes equipped with an action of a reductive group. The emphasis is on examples and applications to the classification of spherical varieties.
The present article aims to provide a brief account of the theories of Drinfeld modules and Anderson's $t$-modules and $t$-motives. As such the article is not meant to be comprehensive, but we have endeavored to summarize aspects of the…
In this paper we study the Grassmannian of submodules of a given dimension inside a finitely generated projective module $P$ for a finite dimensional algebra $\Lambda$ over an algebraically closed field. The orbit of such a submodule $C$…
Let $X$ be a smooth projective and geometrically irreducible curve over the finite field $\mathbb{F}_q$ with $q$ elements and $K$ be its function field. Let $\infty$ be a fixed closed point on $X$ and $A$ be the ring of functions regular…
A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution,…
A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix…
Let $O_D$ be the ring of integers in a division algebra of invariant $1/n$ over a p-adic local field. Drinfeld proved that the moduli problem of special formal $O_D$-modules is representable by Deligne's formal scheme version of the…
The aim of this paper is to investigate the closed subschemes of moduli spaces corresponding to projective varieties which admit an effective action by a given finite group $G$. To achieve this, we introduce the moduli functor…
These are extended notes of a talk given at Maurice Auslander Distinguished Lectures and International Conference (Woods Hole, MA) in April 2013. Their aim is to give an introduction into Schubert calculus on Grassmannians and flag…
The main purpose of this paper is to prove the existence of the moduli space parameterizing the embedded curve singularities of $(k^N,0)$ with an admissible Hilbert polynomial and to study its basic properties.
We prove a generalised version of finiteness of skein modules for 3-manifolds by including boundary. We show that internal skein modules are holonomic modules over the internal skein algebra of the boundary - a property including finite…
By interpreting the product of the Principal Component Analysis, that is the covariance matrix, as a sequence of nested subspaces naturally coming with weights according to the level of approximation they provide, we are able to embed all…
In this paper we develop a general theory of modules which are invariant under automorphisms of their covers and envelopes. When applied to specific cases like injective envelopes, pure-injective envelopes, cotorsion envelopes, projective…
We build an infinite dimensional scheme parametrizing isomorphism classes of coherent quotients of a quasi-coherent sheaf on a projective scheme. The main tool to achieve the construction is a version of Grothendieck's Grassmannian…
Using Quot schemes and a localization theorem we study Gromov-Witten invariants for partial flag varieties. The strategy is to extend A. Bertram's result of Gromov-Witten invariants for special Schubert varieties of Grassmannians to the…
We study the analytic and homotopy properties of some infinite dimensional Grassmannians, useful for developing a Morse theory for infinite dimensional manifolds. We study the space of Fredholm pairs of a Hilbert space, we determine its…
We give a geometric perspective on the algebra of Drinfeld modular forms for congruence subgroups $\Gamma\leq \GL_2(\bbF_q[T]).$ In particular, we describe an isomorphism between the section ring of a line bundle on the stacky modular curve…
We present several principal bundles of embeddings of compact manifolds (with or without boundary) whose base manifolds are nonlinear Grassmannians. We study their infinite dimensional differential manifold structure in the Fr\'echet…
This paper aims at generalizing some geometric properties of Grassmannians of finite dimensional vector spaces to the case of Grassmannnians of infinite dimensional ones, in particular for that of $k((z))$. It is shown that the Determinant…
We prove an analog of Siegel's theorem for integral points in the context of Drinfeld modules. The result holds for finitely generated submodules of the additive group over a function field of transcendence dimension 1.