Related papers: Projective bundle formula for Heller' relative K_0

A projective structure on a compact Riemann surface X of genus g is given by an atlas with transition functions in PGL(2,C). Equivalently, a projective structure is given by a projective sl(2,C)-bundle over X equipped with a section s and a…

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…

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…

In this paper we count the number of isomorphism classes of geometrically indecomposable quasi-parabolic structures of a given type on a given vector bundle on the projective line over a finite field. We give a conjectural cohomological…

For a given stratified bundle $E$ on $X$, we construct an irreducible closed subvariety $\sN(E)_S$ of the so called representation space $R(\sO_{X_S},\xi_S,P)\to S$ such that $\sN(E)_S(\overline{\mathbb{F}}_q)$ contains a dense set of…

We answer a question of Banakh, Jab\l{}o\'nska and Jab\l{}o\'nski by showing that for $d\ge 2$ there exists a compact set $K \subseteq \mathbb{R}^d$ such that the projection of $K$ onto each hyperplane is of non-empty interior, but $K+K$ is…

We construct projectivization of a parabolic vector bundle and a tautological line bundle over it. It is shown that a parabolic vector bundle is ample if and only if the tautological line bundle is ample. This allows us to generalize the…

We introduce a partial positivity notion for algebraic maps via the defect of semismallness. This positivity notion is modeled on $m$-positivity in the analytic setting and $m$-ampleness in the geometric setting. Using this positivity…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

The first goal of the article is to solve several fundamental problems in the theory of holomorphic bundles over non-algebraic manifolds: For instance we prove that stability and semi-stability are Zariski open properties in families when…

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$…

We show a correspondence between the set of all G-invariant projectively flat connections on a homogeneous apace $M=G/K$, and the one of all {G}^~-invariant flat connections on a homogeneous space {M}^~={G}^~/K, where {G}^~ is a central…

We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact K\"ahler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we…

We generalize the higher Riemann-Hilbert correspondence in the presence of scalar curvature for a (possibly non-compact) smooth manifold $M$. We show that the dg-category of curved $\infty$-local systems, the dg-category of graded vector…

Let $K\backslash G$ be an irreducible Hermitian symmetric space of noncompact type and $\Gamma \,\subset\, G$ a closed torsionfree discrete subgroup. Let $X$ be a compact K\"ahler manifold and $\rho\, :\, \pi_1(X, x_0)\,\longrightarrow\,…

Berndtsson's famous theorem asserts that, for a compact K\"ahler fibration $p:X\to Y$, the direct image bundle $p_*(K_{X/Y}\otimes L)$ of a semi-positive Hermitian holomorphic line bundle $L\to X$ is Nakano semi-positive. As a continuation…

Given a full right-Hilbert C*-module $\mathbf{X}$ over a C*-algebra $A$, the set $\mathbb{K}_{A}(\mathbf{X})$ of $A$-compact operators on $\mathbf{X}$ is the (up to isomorphism) unique C*-algebra that is strongly Morita equivalent to the…

In this paper, with the aim of establishing a structure theorem for a compact K\"ahler manifold $X$ with semi-positive holomorphic sectional curvature, we study a morphism $\phi: X \to Y$ to a compact K\"ahler manifold $Y$ with…

Let ${\mathbb F}_0$ be an algebraically closed field, with $char({\mathbb F}_0)=0$. In this article, for prime numbers $p\geq 2$, we construct smooth affine algebras $B$ over ${\mathbb F}_0$, with $\dim B=p+2$. Further, we construct…

We give a complete classification of isomorphism classes of finitely generated projective modules, or equivalently, unitary equivalence classes of projections, over the C*-algebra $C\left( \mathbb{S}_{q}^{2n+1}\right) $ of the quantum…