Related papers: Fibr\'es paraboliques et champ des racines

Let X be an irreducible smooth projective curve defined over complex numbers, S= {p_1, p_2,...,p_n} \subset X$ a finite set of closed points and N > 1 a fixed integer. For any pair (r,d) in Z X Z/N, there exists a parabolic vector bundle…

Given a complex manifold $X$, a normal crossing divisor $D\subset X$ whose irreducible components $D_1,...,D_s$ are smooth, and a choice of natural numbers $r=(r_1,...,r_s)$, we construct a manifold $X(D,\ur)$ with an action of a torus…

Let $D$ be an effective divisor on a smooth projective variety $X$ over an algebraically closed field $k$ of characteristic $0$. We show that there is a one-to-one correspondence between the class of orthogonal (respectively, symplectic)…

Given a projective variety X over an algebraically closed field of characteristic zero, we show that finite parabolic bundles along a fixed simple normal crossings divisor D are in one to one correspondence with representations of the…

Given a variety $X$, and a normal crossings divisor $D\subset X$, we relate, in the case of abelian monodromy, the following two: 1. existence of a $G$-torsor with prescribed ramification, and 2. existence of essentially finite parabolic…

We show that a proper algebraic n-dimensional scheme Y admits nontrivial vector bundles of rank n, even if Y is non-projective, provided that there is a modification containing a projective Cartier divisor that intersects the exceptional…

We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2\le d\leq n-d)$ to be the Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where…

Let X be a smooth projective variety defined over an algebraically closed field k. Nori constructed a category of vector bundles on X, called essentially finite vector bundles, which is reminiscent of the category of representations of the…

Let $C$ be an elliptic curve, $w\in C$, and let $S\subset C$ be a finite subset of cardinality at least $3$. We prove a Torelli type theorem for the moduli space of rank two parabolic vector bundles with determinant line bundle $\mathcal…

Let $E$ be a vector bundle on a smooth complex projective variety $X$. We study the family of sections $s_t\in H^0(E\otimes L_t)$ where $L_t\in Pic^0(X)$ is a family of topologically trivial line bundle and $L_0=\mathcal O_X,$ that is, we…

Given a discrete subgroup $\Gamma$ of finite co-volume of $\mathrm{PGL}(2,\mathbb{R})$, we define and study parabolic vector bundles on the quotient $\Sigma$ of the (extended) hyperbolic plane by $\Gamma$. If $\Gamma$ contains an…

Parabolic SL(r,C)-opers were defined and investigated in [BDP] in the set-up of vector bundles on curves with a parabolic structure over a divisor. Here we introduce and study holomorphic differential operators between parabolic vector…

Let $(X,\,D)$ be an $m$-pointed compact Riemann surface of genus at least $2$. For each $x \,\in\, D$, fix full flag and concentrated weight system $\alpha$. Let $P \mathcal{M}_{\xi}$ denote the moduli space of semi-stable parabolic vector…

Let $X$ be a normal, connected and projective variety over an algebraically closed field $k$. It is known that a vector bundle $V$ on $X$ is essentially finite if and only if it is trivialized by a proper surjective morphism $f:Y\to X$. In…

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

We give a cohomological criterion for a parabolic vector bundle on a curve to be semistable. It says that a parabolic vector bundle $E$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle…

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…

Since Schwarzenberger and his celebrated paper called "Vector bundles on the projective plane" we know that any rank two vector bundle on $\P^2$ is a direct image of a line bundle on a double covering of the plane. This theorem suggests to…

Let N be the moduli space of stable rank 2 quasiparabolic vector bundles of fixed degree on the projective line with 2g+1 marked points, where g>1, and stability is with respect to the weights {0,1/2} at each marked point. In this note we…

We construct vector bundles $R^r_\mu$ on a smooth projective curve $X$ having the property that for all sheaves $E$ of slope $\mu$ and rank $r$ on $X$ we have an equivalence: $E$ is a semistable vector bundle $\iff$ $Hom(R^r_\mu,E)=0$. As a…