Related papers: Rank two vector bundles with canonical determinant

Consider the scheme B_{2,L}^k of stable vector bundles of rank two and fixed determinant L which have at least k sections. Under suitable numerical conditions and for generic L, we show the existence of a component of the expected dimension…

Let $C$ be a smooth irreducible complex projective curve of genus $g$ and let $B^k(2,K_C)$ be the Brill-Noether loci parametrizing classes of (semi)-stable vector bundles $E$ of rank two with canonical determinant over $C$ with…

We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and…

Let C be a smooth projective complex curve of genus $g\geq2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and canonical determinant having at least $k$ independent sections. Using the Hecke correpondence we…

We prove the Bertram-Feinberg-Mukai conjecture for a generic curve $C$ of genus $g$ and a semistable vector bundle $E$ of rank two and determinant $K$ on $C$, namely we prove the injectivity of the Petri-canonical map $S^2(H^0(E))\to…

This paper shows that on the moduli space of semi-stable vector bundles of fixed rank and determinant (of any degree) on a smooth curve of genus at least two, the base locus of the generalized theta divisor is large provided the rank is…

This is a continuation of "Rational families of vector bundles on curves, I". Let C be a smooth projective curve of genus at least 2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1.…

This paper establishes the correctness of a conjecture of Bertram-Feinberg and Mukai for a special class of globally generated rank-two bundles with canonical determinant over a generic Riemann surface of genus at least four.

Let $C$ be a smooth projective complex curve of genus $g \geq 2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and determinant $L$ of odd degree $d$ having at least $k$ independent sections. This locus…

Given any irreducible smooth complex projective curve $X$, of genus at least $2$, consider the moduli stack of vector bundles on $X$ of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the…

We describe the locus of stable bundles on a smooth genus $g$ curve that fail to be globally generated. For each rank $r$ and degree $d$ with $rg<d<r(2g-1)$, we exhibit a component of the expected dimension. We show moreover that no…

We prove that the order of the canonical vector bundle over the configuration space is $2$ for a general planar graph, and is $4$ for a nonplanar graph.

We give an explicit expression of the Hitchin Hamiltonian system for rank two vector bundles with trivial determinant bundle over a curve of genus two.

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…

We give the classification of globally generated vector bundles of rank $2$ on a smooth quadric surface with $c_1\le (2,2)$ in terms of the indices of the bundles, and extend the result to arbitrary higher rank case. We also investigate…

We classify rank two globally generated vector bundles on P^n, n > 2, with c_1 \leq 5. The classification is complete but for one case (n = 3, c_1 = 5, c_2 = 12)

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…

We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces…

Let $X$ be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to…

Let $X$ be a smooth quartic hypersurface in $\mathbb{P}^3$. By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on $X$ is globally generated, then it is the Lazarsfeld-Mukai bundle $E_{C,Z}$ associated with a smooth…