Related papers: A boundedness theorem for principal bundles on cur…

We examine a moduli problem for real and quaternionic vector bundles on a smooth complex projective curve with a fixed real structure, and we give a gauge-theoretic construction of moduli spaces for semi-stable such bundles with fixed…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof of a theorem of Looijenga and…

We define functorial isomorphisms of parallel transport along \'etale paths for a class of principal $G$-bundles on a $p$-adic curve. Here $G$ is a connected reductive algebraic group of finite presentation and the considered principal…

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…

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short…

Let C be an algebraic curve of genus g. Consider extensions E of a vector bundle F'' of rank n'' by a vector bundle F' of rank n'. The following statement was conjectured by Lange: If 0<n'deg F''-n''degF'\le n'n''(g-1), then there exist…

We formulate a conjecture on the behavior of the minimal free resolutions of sets of general points on arbitrary varieties embedded by complete linear series, in analogy with the well-known Minimal Resolution Conjecture for points in…

We give a short proof of the Gauss-Bonnet theorem for a real oriented Riemannian vector bundle $E$ of even rank over a closed compact orientable manifold $M$. This theorem reduces to the classical Gauss-Bonnet-Chern theorem in the special…

Let $G$ be a simple and simply connected complex Lie group, ${\goth{g}}$ its Lie algebra. I remove the restriction ``$G$ is of classical type or $G_2$'' made on $G$ in the papers of Beauville, Laszlo and myself [L-S] and [B-L-S] on the…

In [31,32,33] the Gauss-Bonnet formulas for coherent tangent bundles over compact oriented surfaces (without boundary) were proved. We establish the Gauss-Bonnet theorem for coherent tangent bundles over compact oriented surfaces with…

We prove that the Brauer group of the moduli stack of parabolic stable principal $\text{PGL}(r,\mathbb{C})$-bundles on a curve $X$, for a generic system of weights along an arbitrary parabolic divisor, coincides with the Brauer group of the…

Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. We define the notion of Lie algebroid valued connection on holomorphic principal $G$--bundles on $X$, and study their basic…

We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together…

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…

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent geometry of the surface and the curve. In this paper, we study…

The present paper concerns the invariants of generically nef vector bundles on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka characterization of semistable vector bundles on a curve, the generic nefness can be…

Let $C$ be a smooth projective curve of genus $g\geq 2$. Fix an integer $r\geq 0$, and let $\underline{k}=(k_1,\ldots,k_n)$ be a sequence of positive integers with $k_1+\ldots+k_n=g-1$. We study $n$-pointed curves $(C,p_1,\ldots,p_n)$ such…

Let $G$ be a simple algebraic group of adjoint type over $\mathbb C$, and let $M$ be the wonderful compactification of a symmetric space $G/H$. Take a $\widetilde G$--equivariant principal $R$--bundle $E$ on $M$, where $R$ is a complex…

Let $C$ be a curve over a non-archimedean local field of characteristic zero. We formulate algebro-geometric statements that imply boundedness of functions on the moduli space of stable bundles of rank $2$ and fixed odd degree determinant…