Related papers: Orthogonal bundles over curves in characteristic t…

Let $X$ be a smooth projective curve of genus $g(X)\geq 1$ over an algebraically closed field $k$ of characteristic $p>0$, $\M^s_X(r,d)$ the moduli space of stable vector bundles of rank $r$ and degree $d$ on $X$. We study the Frobenius…

In this paper we proof the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of {\delta}-(semi)stable singular principal G-bundles…

Let X be an irreducible smooth projective curve of genus at least two over an algebraically closed field k of characteristic p>0. In this paper we study the natural stratification, defined using the absolute Frobenius of X, on the moduli…

Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the…

For every $n\geq 3, g\geq 1$ and all large enough $e$ depending on $n,g$, there exist curves of genus $g$, degree $e$ in a general hypersurface of degree $n$ in $\mathbb P^n$, or in $\mathbb P^n$ itself, whose whose normal bundle $N$ is…

In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an…

We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…

Let $C$ be a smooth projective curve of genus $g\ge2$ and let $N$ be the moduli space of stable rank $2$ vector bundles on $C$ of odd degree. We construct a semi-orthogonal decomposition of the bounded derived category of $N$ conjectured by…

Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a…

For a smooth projective curve C with genus g >= 2 and a degree 1 line bundle L on C, let M := SU_{C}(r;L) be the moduli space of stable vector bundles of rank r and with the fixed determinant L. In this paper, we study the small rational…

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 show that a principal G bundle on a smooth projective curve over a finite field is strongly semistable if and only if it is defined by a representation of the fundamental group scheme of the curve into G.

In this short note, we show that any rational curve passing through the generic point in a moduli space of stable bundles with rank $r$ and fixed determinant on a smooth projective curve of genus $g\ge 4$ has degree (with respect to the…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal…

We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and…

This paper treats the strict semi-stability of the symmetric powers $S^k E$ of a stable vector bundle $E$ of rank $2$ with even degree on a smooth projective curve $C$ of genus $g \geq 2$. The strict semi-stability of $S^2 E$ is equivalent…

Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…

We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with…

We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if $V$ is any stable…