Related papers: Cokernel bundles and Fibonacci bundles

Let $X$ be a submanifold of dimension $d\geq 2$ of the complex projective space $\mathbb P^n$. We prove results of the following type. i) If $X$ is irregular and $n=2d$ then the normal bundle $N_{X|\mathbb P^n}$ is indecomposable. ii) If…

We give a cohomological classification of vector bundles of rank $2$ on a smooth affine threefold over an algebraically closed field having characteristic unequal to $2$. As a consequence we deduce that cancellation holds for rank $2$…

In the present paper we study bundles equipped with extra homotopy conditions, in particular so-called simplicial $n$-bundles. It is shown that (under some condition) the classifying space of 1-bundles is the double coset space of some…

Let $X$ be a smooth projective surface over an algebraically closed field $k$ of characteristic $p> 0$ with $\Omega_{X}^{1}$ semistable and $\mu(\Omega_{X}^{1})>0$. For any semistable (resp. stable) bundle $W$ of rank $r$, we prove that…

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…

We define Hecke transformation for orthogonal bundles over a compact Riemann surface. Using the cycles on a moduli space of orthogonal bundles given by Hecke transformations, we prove that the projectivized Picard bundle on the moduli space…

We consider irreducible logarithmic connections $(E,\,\delta)$ over compact Riemann surfaces $X$ of genus at least two. The underlying vector bundle $E$ inherits a natural parabolic structure over the singular locus of the connection…

We obtain the generic real Jordan canonical forms for $n\times n$ matrices with real entries. More precisely, we prove that the set of $n\times n$ real matrices is the union of the closures of $\lfloor n/2\rfloor+1$ sets, which are called…

The moduli space of parabolic bundles with fixed determinant over a smooth curve of genus greater than one is proved to be rational whenever one of the multiplicities associated to the quasi-parabolic structure is equal to one. It follows…

Let $C$ be a smooth irreducible projective curve and $E$ be a rank 2 stable vector bundle on $C$. Then one can associate a rank 4 vector bundle $\mathcal{F}_2(E)$ on $S^2(C)$, second symmetric power of $C$. Our goal in this article is to…

In this paper we show that in a stable range the cohomology of the space of regular algebraic sections of a line bundle $\mathscr{L}$on a curve $X$ is isomorphic to the cohomology of the space of regular $C^{\infty}$sections of the same…

We substantially refine the theory of singular principal bundles introduced in a former paper. In particular, we show that we need only honest singular principal bundles in our compactification. These are objects which carry the structure…

Let $C$ be an algebraic curve of genus $g\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections…

Instanton bundles on $\mathbb{P}^3$ have been at the core of the research in Algebraic Geometry during the last thirty years. Motivated by the recent extension of their definition to other Fano threefolds of Picard number one, we develop…

In this paper we establish the existence of monads on multiprojective spaces $X=\mathbb{P}^{2n+1}\times\mathbb{P}^{2n+1}\times\cdots\times\mathbb{P}^{2n+1}$. We prove stability of the kernel bundle which is a dual of a generalized…

In this paper, we develop canonical bundle formulas for fibrations of relative dimension one in characteristic $p>0$. For such a fibration from a log pair $f\colon (X, \Delta) \to S$, if $f$ is separable, we can obtain a formula similar to…

This work explores the geometry of stable wild Vafa-Witten bundles over the complex projective plane $\mathbb{P}^2$. Specifically, we consider stable rank-two pairs $(E,\Phi)$, with $E\to\mathbb{P}^2$ a rank-two holomorphic vector bundle…

We prove that any vector bundle computing the rank-two Clifford index of a smooth projective algebraic curve is linearly semistable. We also identify conditions under which such bundles become linearly stable, thereby addressing a question…

We characterize those (continuously-normed) Banach bundles $\mathcal{E}\to X$ with compact Hausdorff base whose spaces $\Gamma(\mathcal{E})$ of global continuous sections are topologically finitely-generated over the function algebra…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…