Related papers: Vector Bundles over Normal Varieties Trivialized b…

In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite \'etale after reduction. When $k$ is a real closed field, we prove that such a morphism…

We give a concrete description of the category of G-equivariant vector bundles on certain affine G-varieties (where G is a reductive linear algebraic group over an algebraically closed field of characteristic 0) in terms of linear algebra…

Finitely dominated chain complexes over a Laurent polynomial ring in one indeterminate are characterised by vanishing of their Novikov homology. We present an algebro-geometric approach to this result, based on extension of chain complexes…

In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

Twisted ind-Grassmannians are ind-varieties $\GG$ obtained as direct limits of Grassmannians $G(r_m,V^{r_m})$, for $m\in\ZZ_{>0}$, under embeddings $\phi_m:G(r_m,V^{r_m})\to G(r_{m+1}, V^{r_{m+1}})$ of degree greater than one. It has been…

Fujita's second theorem for K\"ahler fibre spaces over a curve asserts that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. We focus on our…

This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…

Let $G$ be a split reductive group over a finite field $k$. In this note we study the space $V$ of finitely supported functions on the set of isomorphism classes $G$-bundles on the projective line ${\mathbb P}^1$ endowed with a…

We study the birationality (onto its image) of the Abel-Prym morphism associated with a Prym-Tuyrin variety. We use such result to prove that Picard bundles over Prym varieties are simple and moreover they are stable when the Abel-Prym…

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$,…

Let $X$ be a normal projective variety over an algebraically closed field of characteristic zero. Let $D$ be a reduced Weil divisor on $X$. Let $G$ be a reductive linear algebraic group. We introduce the notion of a logarithmic connection…

The stratified vector bundles on a smooth variety defined over an algebraically closed field $k$ form a neutral Tannakian category over $k$. We investigate the affine group--scheme corresponding to this neutral Tannakian category.

Let $\Cal E$ be a very ample vector bundle of rank two on a smooth complex projective threefold $X$. An inequality about the third Segre class of $\Cal E$ is provided when $K_X+\det \Cal E$ is nef but not big, and when a suitable positive…

Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \mathrm{Sym}^2(V) \ra \mathcal{O}_X$ (respectively symplectic form $q: \Lambda^2V \ra \mathcal{O}_X$). Fixing the degeneracy locus of the…

It is conjectured by de Jong that, if $X$ is a connected projective smooth variety over an algebraically closed field $k$ of characteristic $p>0$ with trivial etale fundamental group, any convergent isocrystal $\mathcal{E}$ on $X$ is…

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 propose a matrix regularization of vector bundles over a general closed K\"ahler manifold. This matrix regularization is given as a natural generalization of the Berezin-Toeplitz quantization and gives a map from sections of a vector…

We first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety. Then we show that very few connected algebraic semigroups can be realized as…

We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization…