相关论文: Rank two bundles on P^n with isolated cohomology

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.…

For $n\geq 3$ and $r\geq n$, we show that there are rank-$r$ vector bundles on $\mathbb{P}^n$ with arbitrary homological dimension. We apply the Bernstein-Gel'fand-Gel'fand correspondence to translate the vector bundle question into a…

Assume that $G$ is a virtually torsion-free solvable group of finite rank and $A$ a $\mathbb ZG$-module whose underlying abelian group is torsion-free and has finite rank. We stipulate a condition on $A$ that ensures that $H^n(G,A)$ and…

We prove stability of the kernel bundle and prove that the cohomology bundle is simple for vector bundles associated to monads on $X = (\mathbb{P}^{n_1})^2\times\cdots\times(\mathbb{P}^{n_s})^2$ for an ample line bundle…

We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of…

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…

We give a formula comparing the E-series of the moduli stacks of rank 2 degree 0 semistable Higgs bundles in genus $g \geq 2$ to intersection E-polynomials of its coarse moduli space. A parellel formula holds in various 2-Calabi-Yau…

We study the motive of the moduli spaces of semistable rank two vector bundles over an algebraic curve. When the degree is odd the moduli space is a smooth projective variety, we obtain the absolute Hodge motive of this, and in particular…

We show that all filtrable bundles on a Hopf surface $X$ must have jumps and we prove the existence of filtrable stable bundles on $X$ with any value of $c_2>0$. On a somewhat opposite direction, for each integer $r\ge 2$ we prove the…

Holomorphic vector bundles on $\mathbb C\times M$, $M$ a complex manifold, with meromorphic connections with poles of Poincar\'e rank 1 along $\{0\}\times M$ arise naturally in algebraic geometry. They are called $(TE)$-structures here.…

In order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such…

We are interested in those bundles $C$ on $\mathbb{P}^N$ which admit a resolution of the form $$ 0 \to \mathbb{C}^s \otimes E \xrightarrow{\mu} \mathbb{C}^t \otimes F \to C \to 0.$$ In this paper we prove that, under suitable conditions on…

We give an almost complete classification of Ulrich bundles $\mathcal E$ with $c_2(\mathcal E)^2=0$ on a variety $X$ of dimension $n \ge 4$. Moreover, we show that there are strong constraints on the geometry of $X$ and we study…

It has been observed, by S. Rayan, that the complex projective surfaces that potentially admit non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the Enriques-Kodaira classification. Motivated by this…

We prove the following result : Let $E$ be a rank 2 bundle on ${\bf P}$, the projective space of dimension 3, and $n$ a relative number such that $H^0E(n-1)=0$ and $H^0E(n)\neq 0$. Let $C$ be a curve which is the zero locus of a section of…

Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant. We prove that an H-equivariant holomorphic vector bundle…

Let $X$ be a smooth variety defined over an algebraically closed field of arbitrary characteristic and $\O_X(H)$ be a very ample line bundle on $X$. We show that for a semistable $X$-bundle $E$ of rank two, there exists an integer $m$…

In this note, we give a cohomological characterization of all rank 2 split vector bundles on Hirzebruch surfaces.

We study the moduli space of parabolic connections of rank two on the complex projective line $\mathbb{P}^1$ minus five points with fixed spectral data. This paper aims to compute the cohomology of the structure sheaf and a certain vector…

We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of K\"ahler solvmanifolds as…