Related papers: Rank 2 arithmetically Cohen-Macaulay bundles on a …

We study rank 3 stable bundles E on P^3 as extensions of a line bundle B on a smooth surface S in P^3 by the direct sum of three copies of O_{P^3}(-\nu). In most cases, S (the dependency locus of three sections of E(\nu)) lies in the…

In this paper we study ACM vector bundles $\E$ of rank $k \geq 3$ on hypersurfaces $X_r \subset\Pj^4$ of degree $r \geq 1$. We consider here mainly the case of degree $r = 4$, which is the first unknown case in literature. Under some…

Let $F\subseteq\mathbb P ^{a+1}$ be a non-degenerate $K3$ surface of degree $2a$, where $a\ge2$. In this paper we deal with Ulrich bundles on $F$ of rank $2$. We deal with their stability and we construct $K3$ surfaces endowed with families…

We show that Horrocks' criterion for the splitting of rank two vector bundles in P^3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P^4. Extension of other splitting criterion are studied.

Let $S \subset \mathbb P^3$ be a very general sextic surface over complex numbers. Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In this…

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used…

Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all possible Chern classes of stable vector bundles.

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…

ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the rational normal curves that they contain. A complete list of ACM line bundles is provided. Moreover, for any del Pezzo surface $X$ of degree less or equal than six and…

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…

Let $F\subseteq\mathbb{P}^3$ be a smooth determinantal quartic surface which is general in the N\"other-Lefschetz sense. In the present paper we give a complete classification of locally free sheaves $\mathcal{E}$ of rank $2$ on $F$ such…

In this paper we continue our study of the moduli space of stable bundles of rank two and degree 1 on a very general quintic surface. The goal in this paper is to understand the irreducible components of the moduli space in the first case…

In this paper we show that on a general hypersurface of degree $r=3,4,5,6$ in ${\bf P}^5$ a rank 2 vector bundle $E$ splits if and only if $h^1 E(n)=h^2 E(n)=0$ for all $n \in \bf Z$.

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…

In this short note, we observe that Theorem 3.1 in arXiv:1508.00682 for semiorthogonal indecomposability of the derived category of smooth DM stacks based on the canonical bundle can be extended to the case of projective varieties with…

In this paper we give the classification of rank 3 vector bundles without "inner" cohomology on a quadric hypersurface \Q_n (n>3) by studying the associated monads.

Let $k$ be a number field and $\mathcal{E}$ an elliptic curve defined over the function field $k(T)$ given by an equation of the form $y^2 = a_3x^3 + a_2x^2 + a_1x + a_0$, where $a_i \in k[T]$ and $deg(a_i) \leq 2$. We explore the conic…

We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector…

We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank 2, which appears in the definition of noncommutative…

We construct a rank-$2$ indecomposable vector bundle on $\mathbb P^2\times\mathbb P^2$ in characteristic $2$ that does not come from a bundle on $\mathbb P^2$ by factor projection nor from a bundle on $\mathbb P^{m} $ by central projection.…