相关论文: Grassmannian of $k((z))$: Picard Group, Equations …

Motivated by the theory of locally definable groups, we study the theory of $K$-vector spaces with a predicate for the union $X$ of an infinite family of independent subspaces. We show that if $K$ is infinite then the theory is complete and…

Let A be an algebra over a field k, and denote by D^b(Mod A) the bounded derived category of left A-modules. The derived Picard group DPic_k(A) is the group of triangle auto-equivalences of D^b(Mod A) induced by tilting complexes. We study…

We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent bundle. This description is based on the hypergeometric…

The present work completes the classification of the compact Riemann surfaces of genus g with an analytic automorphism of order p (prime number) and p > g. More precisely, we construct a parameteriza- tion space for them, we compute their…

We study Picard groups and Picard functors of perfectoid spaces which are limits of rigid spaces. For sufficiently large covers that are limits of rigid spaces of good reduction, we show that the Picard functor can be represented by the…

We investigate similarities between the category of vector spaces and that of polytopal algebras, containing the former as a full subcategory. In Section 2 we introduce the notion of a polytopal Picard group and show that it is trivial for…

In this paper, we construct explicitely polynomial automorphisms of affine n-space for certain n. More precisely, we construct algebraic subgroups of the general polynomial group GA_n(k) where k is an arbitrary base ring of characteristic…

Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of…

This work revolves around the question of whether a given resonance variety is associated with a vector bundle. We show the existence of a family of natural morphisms on a stratification of the resonance variety to a suitable family of a…

The purpose of this of this paper is to develop the theory of Eisenstein series in the framework of geometric Langlands correspondence. Our construction is based on the study of certain relative compactification of the moduli stack of…

The Plucker relations define a projective embedding of the Grassmann variety Gr(k,n). We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6. This is achieved by constructing a…

Correlation functions can be calculated on Riemann surfaces using the operator formalism. The state in the Hilbert space of the free field theory on the punctured disc, corresponding to the Riemann surface, is constructed at infinite genus,…

Several moduli spaces parametrizing linear subspaces of the projective space are cut out by linear and quadratic equations in their natural embedding: Grassmannians, Flag varieties, and Schubert varieties. The goal of this paper is to prove…

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…

We show that a linear algebraic group is the Galois group of a parameterized Picard-Vessiot extension of k(x), x' = 1, for certain differential fields k, if and only if its identity component has no one dimensional quotient as a linear…

In this paper the classification of left-invariant Riemannian metrics, up to the action of the automorphism group, on cotangent bundle of (2n+1)-dimensional Heisenberg group is presented. Also, it is proved that the complex structure on…

For a certain class of abelian categories, we show how to make sense of the "Euler characteristic" of an infinite projective resolution (or, more generally, certain chain complexes that are only bounded above), by passing to a suitable…

We prove a theorem classifying the equivariant $K$-theoretic pushforwards of the product of arbitrary Schur functors applied to the tautological bundle on the moduli space of framed rank $r$ torsion-free sheaves on $\mathbb{P}^2$, and its…

This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The…

The Grassmannian, which is the manifold of all $k$-dimensional subspaces in the Euclidean space $\mathbb{R}^n$, was decomposed through three equivalent methods connecting combinatorial geometries, Schubert cells and convex polyhedra by…