Related papers: On partially ample Ulrich bundles

We study the Teichm\"uller space of negatively curved metrics on a high dimensional manifold, with applications to bundles with negatively curved fibers.

In this paper, we study equivariant vector bundles on partial flag varieties arising from Schur functors. We show that a partial flag variety with three or more steps does not admit an Ulrich bundle of this form with respect to the minimal…

We show that Cuntz--Pimsner algebras associated to partial automorphisms twisted by vector bundles are classifiable in the sense of the Elliott program whenever the action is minimal and the base space is compact, infinite and has finite…

Let X_R be a geometrically irreducible smooth projective curve, defined over R, such that X_R does not have any real points. Let X= X_R\times_R C be the complex curve. We show that there is a universal real algebraic line bundle over X_R x…

Let $X^n\subset C^{n+a}$ or $X^n\subset P^{n+a}$ be a patch of an analytic submanifold of an affine or projective space, let $x\in X$ be a general point, and let L^k be a linear space of dimension k osculating to order m at x. If m is large…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

The q-monopole bundle introduced previously is extended to a general construction for quantum group bundles with non-universal differential calculi. We show that the theory applies to several other classes of bundles as well, including…

We describe a locally trivial quantum principal U(1)-bundle over the quantum space S^2_{pq} which is a noncommutative analogue of the usual Hopf bundle. We also provide results concerning the structure of its total space algebra…

Let $\mathcal{X} \subset \mathbb{P}_k^d$ be Drinfeld's halfspace over a finite field $k$ and let $\mathcal{E}$ be a homogeneous vector bundle on $\mathbb{P}_k^d$. The paper deals with two different descriptions of the space of global…

Let $X$ be a smooth projective scheme and $E$ a vector bundle on $X$. For a relative hypersurface $Y_f \subset \mathbb{P}(E)$ of degree $d$ defined by a global section $f$, we establish a functorial equivalence between the category of…

Let $(L,he^{-u})$ be a pseudoeffective line bundle on an $n$-dimensional compact K\"ahler manifold $X$. Let $h^0(X,L^k\otimes \mathcal I(ku))$ be the dimension of the space of sections $s$ of $L^k$ such that $h^k(s,s)e^{-ku}$ is integrable.…

We study the classification of affine holomorphic bundles over a compact complex manifold $X$ in general, and we apply the general theory to the case $X=\mathbb{P}^1_\mathbb{C}$. We study the moduli space of framed, non-degenerate rank 2…

Apart from math.AG/0608569, it contains the following applications of it. Let M be a simply connected, irreducible smooth complex projective variety of dimension $n$ such that the Picard number of $M$ is one. If the canonical line bundle…

Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles…

We study flat vector bundles over complex parallelizable manifolds.

We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the…

In this article, we solve the problem of constructing moduli spaces of semistable principal bundles (and singular versions of them) over smooth projective varieties over algebraically closed ground fields of positive characteristic.

Let $X={\bf P}^2\times{\bf P}^{n-1}$ embedded with $\O(1,2)$. We prove that its $(n+1)$-secant variety $\sigma_{n+1}(X)$ is a hypersurface, while it is expected that it fills the ambient space. The equation of $\sigma_{n+1}(X)$ is the…

Suppose $P^n_m$ is the blow up of $\mathbb{P}^n$ at a linear subspace of dimension $m$, $\mathcal{L}=\{L_1,\ldots,L_r\}$ is a (not necessarily full) strong exceptional collection of line bundles on $P^n_m$. Let $Q$ be the quiver associated…

This paper deals with two problems about vector bundles on bielliptic surfaces. The first is to give a classification of Ulrich bundles on such surfaces $S$, which depends on the topological type of $S$. In doing so, we study the weak…