Related papers: Parabolic Raynaud bundles

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…

In this paper we study the extension of structure group of principal bundles with a reductive algebraic group as structure group on smooth projective varieties defined over algebraically closed field of positive characteristic. Our main…

It is a longstanding problem in Algebraic Geometry to determine whether the syzygy bundle $E_{d_1,..., d_n}$ on $\PP^N$ defined as the kernel of a general epimorphism $\xymatrix{\phi:\cO(-d_1)\oplus...\oplus\cO(-d_n)\ar[r] &\cO}$ is…

Let $M$ be a quasi-regular compact connected Sasakian manifold, and let $N = M/S^1$ be the base projective variety. We establish an equivalence between the class of Sasakian $G$-Higgs bundles over $M$ and the class of parabolic (or…

Let X be a smooth complex projective curve and S a finite subset of X. We show that an orthogonal or symplectic parabolic Higgs bundle on X with parabolic structure over S admits a Hermitian-Einstein connection if and only if it is…

Let $B$ be a simply-connected projective variety such that the first cohomology groups of all line bundles on $B$ are zero. Let $E$ be a vector bundle over $B$ and $X={\mathbb P} (E)$. It is easily seen that a power of any endomorphism of…

Consider a smooth projective curve C of genus g over a complete discrete valuation field of characteristic 0 and residue field \Fbar_p. Motivated by Narasimhan and Seshadri's theorem, Faltings asked whether all semistable vector bundles of…

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over…

In this paper, we consider the weight $i$ de Rham--Gauss--Manin bundles on a smooth variety arising from a smooth projective morphism $f:X\_U\lrar U$ for $i\geq 0$. We associate to each weight $i$ de Rham bundle, a certain parabolic bundle…

Given a smooth complex projective variety X and a smooth divisor D on X, we prove the existence of Hermitian-Einstein connections, with respect to a Poincar\'e-type metric on X - D, on polystable parabolic principal Higgs bundles with…

The Hilbert scheme of n points in the projective plane parameterizes degree n zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying…

We study the positivity properties of the projectivization of a parabolic bundle over a smooth complex projective curve. The generators of its N\'eron--Severi group are computed, and the positive cone is determined. In particular, we…

In this paper we obtain bounds on $h^0(E)$ where $E$ is a semistable bundle of rank 3 over a smooth irreducible projective curve $X$ of genus $g \geq 2$ defined over an algebraically closed field of characteristic 0. These bounds are…

We define SL(r)-opers in the set-up of vector bundles on curves with a parabolic structure over a divisor. Basic properties of these objects are investigated.

For a given graph whose edges are labeled with general real numbers, we consider the set of functions from the vertex set into the Euclidean plane such that the distance between the images of neighbouring vertices is equal to the…

Let f : X --> Spec(Z) be an arithmetic variety of dimension d >= 2 and (H, k) an arithmetically ample Hermitian line bundle on X. Let (E, h) be a rank r vector bundle on X. In this paper, we will prove that if E is semistable with respect…

Let $E$ be the Whitney sum of complex line bundles over a topological space $X$. Then, the projectivization $P(E)$ of $E$ is called a \emph{projective bundle} over $X$. If $X$ is a non-singular complete toric variety, so is $P(E)$. In this…

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

The moduli space M(n,d) is an algebraic variety parametrizing those representations of the fundamental group of a punctured Riemann surface into the Lie group SU(n) for which a loop around the boundary is sent to the n-th root of unity exp…

Absolutely indecomposable vector bundle and parabolic vector bundles are well-studied via quiver representations. In this paper, we study absolutely indecomposable quasi-parabolic $G$-bundles over $\mathbb{P}^1$ with generic additive…