Related papers: Affine holomorphic bundles over $\mathbb{P}^1_\mat…

Let $X$ be an ordinary smooth curve defined over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the moduli space $M_X$ of rank 2 vector bundles with fixed trivial determinant. If the…

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve; we study the moduli problem of parametrizing certain pairs consisting of a sheaf E on S and a map of E to a fixed reference sheaf on…

We study the locus of smooth hypersurfaces inside the Hilbert scheme of a smooth projective complex variety. In the spirit of scanning, we construct a map to a continuous section space of a projective bundle, and show that it induces an…

It is in general unknown which topological complex vector bundles on a non-algebraic surface admit holomorphic structures. We solve this problem for primary Kodaira surfaces by using results of Kani on curves of genus two with elliptic…

In this note we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\PP^{2n+1}}$, defined from the well known monad condition, is affine. This result was not known even in the case $n=1$, where the real instanton…

We study stable vector bundles over the modular curve X(p) corresponding to the principal congruence subgroup of the modular group of prime level p which are invariant with respect to its automorphism group.

Let $p_E : E \to M$ be a fibre bundle over the $m$-dimensional manifold $M$ whose typical fibre is the vector space $\R^e$ and let $p_F : F \to N$ be a fibre bundle over the $n$-dimensional manifold $N$ whose typical fibre is the vector…

This paper classifies rank two vector bundles on a del Pezzo threefold $X$ of degree five whose projectivizations are weak Fano. This classification is then used to determine properties of the moduli spaces of such vector bundles on $X$,…

Let $k$ be an algebraically closed field with characteristic $2$, and let $X$ be a smooth projective algebraic curve of genus $g \geqslant 2$ over $k$. Let $\mathcal{M}^s_X(2,\mathcal{L})$ be the moduli space of rank $2$ stable vector…

The character varieties of representations of a surface group into the Lie groups SL(m,H), SO(2m,H) and Sp(m,m) have a holomorphic description in terms of the moduli space of Higgs bundles. We show that the fibres of the integrable system…

Let P^n be the projective space of dimension n on an algebraically closed field of characteristic 0 and F be the image of the Segre embedding of P^1xP^1xP^1 inside P^7. In the present paper we deal with the moduli spaces of locally free…

Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_X-coherent D_X-modules) on X without relying on…

We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection. These structures arise in connection to the moduli space of heterotic…

This work concerns the problem of relating characteristic numbers of one-dimensional holomorphic foliations of P^n to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional…

We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…

We consider the moduli spaces of flat $SL(n, C)$-bundles on Riemann surfaces with one puncture when we fix the conjugacy class ${\cal C}$ of the monodromy transformation around the puncture. We show that under a certain condition on the…

Let $E$ be a vector bundle of rank $r\geq 2$ on a smooth projective curve $C$ of genus $g \geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\le k\le r-1$ we define $${\se}_k(E):=k\deg…

We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with…

We study simply-laced simple affine Lie algebra bundles over complex surfaces X. Given any Kodaira curve C in X, we construct such a bundle over X. After deformations, it becomes trivial on every irreducible component of C provided that…

In this paper we show that in a stable range the cohomology of the space of regular algebraic sections of a line bundle $\mathscr{L}$on a curve $X$ is isomorphic to the cohomology of the space of regular $C^{\infty}$sections of the same…