Related papers: Parabolic Raynaud bundles

We determine some classes of varieties X - that include the varieties with numerically effective tangent bundle - satisfying the following property: if E is a Higgs bundle such that f*E is semistable for any morphism f from a smooth…

Let $X$ be a submanifold of dimension $d\geq 2$ of the complex projective space $\mathbb P^n$. We prove results of the following type. i) If $X$ is irregular and $n=2d$ then the normal bundle $N_{X|\mathbb P^n}$ is indecomposable. ii) If…

A lot is known about the moduli space of parabolic bundles over curves of genus $g\geq 2$, but the lower genus cases are notably different. The goal of this article is to study the geometry of the moduli space of semistable parabolic…

According to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles:…

Given a geometrically irreducible smooth projective curve of genus 1 defined over the field of real numbers, and a pair of integers r and d, we determine the isomorphism class of the moduli space of semi-stable vector bundles of rank r and…

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)…

This note is an attempt to generalize Bolibruch's theorem from the projective line to curves of higher genus. We show that an irreducible representation of the fundamental group of an open in a curve of higher genus has always a…

Given a vector bundle $E$ on a complex reduced curve $C$ and a subspace $V$ of $H^0(E)$ which generates $E$, one can consider the kernel of the evaluation map $ev_V:V\otimes \mathcal{O}_C\to E$, i.e. the {\it kernel bundle } $M_{E,V}$…

Let $f : X \rightarrow Y$ be a separable finite surjective map between irreducible normal projective varieties defined over an algebraically closed field, such that the corresponding homomorphism between \'etale fundamental groups $f_* :…

Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $\xi$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, \alpha)$ (respectively, $\mathcal{M}_{pc}(r, \alpha,…

In this paper, we study rank 2 (quasi) parabolic bundles over the Riemann sphere with an effective divisor and these moduli spaces. First we consider a criterium when a parabolic bundle admits a unramified irregular singular parabolic…

We prove that for an irreducible representation $\tau:GL(n)\to GL(W)$, the associated homogeneous ${\bf P}_k^n$-vector bundle $W_{\tau}$ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in ${\bf P}_k^n$,…

Sommese has conjectured a classification of smooth projective varieties X containing, as an ample divisor, a P^d-bundle Y over a smooth variety Z. This conjecture is known if d>1, if dim(X)<5, or if Z admits a finite morphism to an Abelian…

Let $(E,\varphi)$ be decorated vector bundle of type $(a,b,c,N)$ on a smooth projective curve $X$. There is a suitable semistability condition for such objects which has to be checked for any weighted filtration of $E$. We prove, at least…

We consider principal bundles over homogeneous spaces G/P, where P is a parabolic subgroup of a semisimple and simply connected complex linear algebraic group G. We prove that a holomorphic principal H--bundle, where H is a complex…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

We observe that the E-resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at…

The goal of this paper is the study of simple rank 2 parabolic vector bundles over a $2$-punctured elliptic curve $C$. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to $\mathbb{P}^1 \times…

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…