Related papers: On Pursell-Shanks type results

We associate a $C^*$-algebra to a partial action of the integers acting on the base space of a vector bundle, using the framework of Cuntz--Pimsner algebras. We investigate the structure of the fixed point algebra under the canonical gauge…

We prove that the modular component $\mathcal M(r)$, constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank $r$ and given Chern classes,…

We apply ourselves to the noncommutative geometry of frame bundles by showing that each C$^*$-algebraic noncommutative principal $\mathrm{SO}(n)$-bundle is, up to isomorphism, uniquely determined by its associated noncommutative vector…

In this article, we develop a version of Sen theory for equivariant vector bundles on the Fargues-Fontaine curve. We show that every equivariant vector bundle canonically descends to a locally analytic vector bundle. A comparison with the…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

This paper is devoted to the study of the family of morphisms of vector bundle, defined by the systems equivalence to linear differential equations. It is proved, that the specified families of the morphisms of vector bundle is not…

This monograph is devoted to the theory of vector-valued modular forms for orthogonal groups of signature (2,n). Our purpose is multi-layered: (1) to lay a foundation of the theory of vector-valued orthogonal modular forms; (2) to develop…

Let $\pi:Y\to X$ be a surjective morphism between two irreducible, smooth complex projective varieties with ${\rm dim}Y>{\rm dim}X >0$. We consider polarizations of the form $L_c=L+c\cdot\pi^*A$ on $Y$, with $c>0$, where $L,A$ are ample…

We prove an analogue of Kac's Theorem, describing the dimension vectors of indecomposable coherent sheaves, or parabolic bundles, over weighted projective lines. We use a theorem of Peng and Xiao to associate a Lie algebra to the category…

Let X be a very general Debarre-Voisin fourfold. In this article, we prove that all the Schur functors of the restriction of the quotient bundle of Gr(6,10) to X are modular and polystable vector bundles. We also show that such bundles are…

We prove that the class of principal coactions is closed under one-surjective pullbacks in an appropriate category of algebras equipped with left and right coactions. This allows us to handle cases of C*-algebras lacking two different…

We review the definition of a Lie manifold $(M, \VV)$ and the construction of the algebra $\Psi\sp{\infty}\sb{\VV}(M)$ of pseudodifferential operators on a Lie manifold $(M, \VV)$. We give some concrete Fredholmness conditions for…

The Serre-Swan theorem in differential geometry establishes an equivalence between the category of smooth vector bundles over a smooth compact manifold and the category of finitely generated projective modules over the unital ring of smooth…

In this paper we prove that, for every $r \geq 2$, the moduli space $M^s_X(r;c_1,c_2)$ of rank $r$ stable vector bundles with Chern classes $c_1=rH$ and $c_2=(3r^2-r)/2$ on a nonsingular cubic surface $X \subset \mathbb{P}^3$ contains a…

In this paper we give top most and least indices of non vanishing cohomology modules of line bundles in the Kac Moody setting in terms of Weyl group combinatorics. We also prove a surjection Theorem.

We study hyperbolicity properties of the moduli space of polarized abelian varieties (also known as the Siegel modular variety) in characteristic $p$. Our method uses the plethysm operation for Schur functors as a key ingredient and…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

We demonstrate the existence of a uniform and nonhomogeneous vector bundle $E$ of rank $(n-d)(m+1)-1$ over Grassmannian $\mathbb{G}(d,n)$, where $m>d$ and $1\le d \le n-d-1$ with a $\mathbb{P}$-homogeneity degree $h(E)=d$. Particularly, we…

Let M be the moduli space of SO(r)-bundles on a curve, and L the determinant bundle on M. We define an isomorphism of H^0(M,L) onto the dual of the space of r-th order theta functions on the Jacobian of C. This isomorphism identifies the…

Let $C$ be a smooth irreducible projective curve of genus $g$ and $L$ a line bundle of degree $d$ generated by a linear subspace $V$ of $H^0(L)$ of dimension $n+1$. We prove a conjecture of D. C. Butler on the semistability of the kernel of…