Related papers: Rank four vector bundles without theta divisor ove…

In this paper, it is proved that certain stable rank-3 vector bundles can be written as extensions of line bundles and stable rank-2 bundles. As an application, we show the rationality of certain moduli spaces of stable rank-3 bundles over…

We study the moduli space of stable sheaves of Euler characteristic 2, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers and we give a…

We present a new class of examples of base points for the generalized theta divisor on the moduli space of semistable vector bundles of trivial determinant on a compact Riemann surface and we prove that for sufficiently large rank the base…

Let $C$ be a hyperelliptic curve of genus $g\geq 3$. In this paper we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on $C$ with trivial determinant. In order to do this, we describe…

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…

Let $M$ denote the moduli space of stable vector bundles of rank $n$ and fixed determinant of degree coprime to $n$ on a non-singular projective curve $X$ of genus $g \geq 2$. Denote by $\cU$ a universal bundle on $X \times M$. We show…

Let (X,H) be a polarized smooth projective surface satisfying H^1(X,O_X)=0 and let F be either a rank one torsion-free sheaf or a rank two {\mu}H-stable vector bundle on X. Assume that c_1(F)/=0. In this article it is shown that the rank…

The variety of minimal rational tangents associated to Hecke curves was used by J.-M.Hwang [8] to prove the simplicity of the tangent bundle on the moduli of vector bundles over a curve. In this paper, we use the tangent maps of the…

Let $X$ be a smooth projective complex curve of genus $g \geq 2$ and let $\M_X(2,\Lambda)$ be the moduli space of semi-stable rank-$2$ vector bundles over $X$ with fixed determinant $\Lambda$. We show that the wobbly locus, i.e., the locus…

We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at…

We show the stability of certain syzygies of line bundles on curves, which we call transforms, and are kernels of the evaluation map on subspaces of the space of global sections. For the transforms constructed, we prove the existence of…

Given a rank $r$ stable bundle over a smooth irreducible projective curve $C,$ there is an associated rank $2r$ bundle over $S^2(C),$ the second symmetric power of $C.$ In this article we study the stability of this bundle. As a consequence…

In this paper, we study the $(k,l)$-stable vector bundles over non-singular projective curve $X$ of genus $g\geq 2,$ its relation with stability and Segre invariants. For rank 2 and 3, we give an explicit description and relation of…

In this paper we study the relationship between two different compactifications of the space of vector bundle quotients of an arbitrary vector bundle on a curve. One is Grothendieck's Quot scheme, while the other is a moduli space of stable…

Let $C$ be a chain-like curve over $\mathbb{C}$. In this paper, we investigate the rationality of moduli spaces of $w$-semistable vector bundles on $C$ of arbitrary rank and fixed determinant by putting some restrictions on the Euler…

Let X be a complex projective curve which is smooth and irreducible of genus 2. The moduli space M_2 of semistable symplectic vector bundles of rank 4 over X is a variety of dimension 10. After assembling some results on vector bundles of…

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…

For any standard quadric surface bundle over $\mathbb P^2$, we show that the locus of rational fibres is dense in the moduli space.

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…