Related papers: On initialized and ACM line bundles over a smooth …

We discuss the hypersurfaces of the moduli spaces of rank $2$ vector bundles on a classical Hopf surface formed by irregular bundles.

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 propose the definition of $\ell$-away ACM bundle on a polarized variety $(X, \mathcal{O}_{X}(h))$. Then we give constructions of $\ell$-away ACM bundles on $(\mathbb{P}^2 , \mathcal{O}_{\mathbb{P}^2}(1))$, $(\mathbb{P}^1 \times…

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…

In this article we study asymptotic slopes of strongly semistable vector bundles on a smooth projective surface. A connection between asymptotic slopes and strong restriction theorem of a strongly semistable vector bundle is shown. We also…

This note will become part of a new paper with more authors.

Let $X$ be a smooth hypersurface of degree $d$ in $\CP^3$. By totally algebraic calculations, we prove that on the third Demailly-Semple jet bundle $X_3$ of $X$, the bundle $\ocal_{X_3}(1)$ is big for $d\geq 11$, and that on the fourth…

We study the moduli space $\fM^s(6;3,6,4)$ of simple rank 6 vector bundles $\E$ on $\PP^3$ with Chern polynomial $1+3t+6t^2+4t^3$ and properties of these bundles, especially we prove some partial results concerning their stability. We first…

We prove that any rank two arithmetically Cohen-Macaulay vector bundle on a general hypersurface of degree at least three in $\mathbb{P}^5$ must be split.

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 X be a smooth hypersurface in projective space. We discuss in this paper when X can be defined by an equation det M = 0 (resp. pf M = 0), where M is a matrix (resp. a skew-symmetric matrix) with homogeneous entries. Standard homological…

Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to semistable bundles of any rank. Recent work has been focussed mainly on the…

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable…

We give a partial positive answer to a conjecture of Tyurin (\cite {Tyu}). Indeed we prove that on a general quintic hypersurface of $\Pj^4$ every arithmetically Cohen--Macaulay rank 2 vector bundle is infinitesimally rigid.

We define the isomorphism classes of torus-equivariant rank 2 arithmetically Cohen-Macaulay (aCM) vector bundles on the Veronese surface, up to a twist by the hyperplane class, and count them. Our approach makes use of Klyachko's…

In this paper, we say that a rank 2 bundle splits if it is given by an extension of two line bundles. In the previous works, we gave a necessary condition for Lazarsfeld-Mukai bundles of rank 2 to split, under a numerical condition ([W2],…

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let $\L=\mathcal O_{\mathbb P^N}(1)|_X$ denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of $\L$ are…

We study geometric properties of characteristic classes of surfaces bundles. In particular, we show that oriented surface bundles over bases with amenable fundamental groups and dimension at least 2 have trivial simplicial volume. We show…

We introduce a local coordinate description for the correspondence between the space of oriented affine lines in Euclidean ${\Bbb{R}}^3$ and the tangent bundle to the 2-sphere. These can be utilised to give canonical coordinates on surfaces…