Related papers: Linear and Steiner bundles on projective varieties

In the present article we work out a relative setup of generic structures on surface singularities. We fix an analytic type on a subgraph of a rational homology sphere resolution graph $\mathcal{T}$ and we choose a relatively generic normal…

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…

This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…

We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties $X$ and $Y$ in dual projective spaces are…

We prove a general result about the geometry of holomorphic line bundles over Kahler manifolds.

Tautological bundles of realizations of matroids were introduced in [BEST23] as a unifying geometric model for studying matroids. We compute the cohomologies of exterior and symmetric powers of these vector bundles, and show that they…

Using Bridgeland stability conditions we give sufficient criteria for a stable vector bundle on a surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the…

We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov's treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3…

For line bundles on arithmetic varieties we construct height functions using arithmetic intersection theory. In the case of an arithmetic surface, generically of genus g, for line bundles of degree g equivalence is shown to the height on…

We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.

Some cohomology elements, called $\nu$ classes, as a supergeneralization of universal Chern classes, are introduced for canonical super line bundles over $\nu$ projective spaces, a novel supergeometric generalization of projective spaces.…

We call a sheaf on an algebraic variety immaculate if it lacks any cohomology including the zero-th one, that is, if the derived version of the global section functor vanishes. Such sheaves are the basic tools when building exceptional…

Let $X$ be a smooth quintic hypersurface in $\mathbb{P}^3$, let $C$ be a smooth hyperplane section of $X$, and let $H=\mathcal{O}_X(C)$. In this paper, we give a necessary and sufficient condition for the line bundle given by a non-zero…

We study holomorphic locally homogeneous geometric structures modelled on line bundles over the projective line. We classify these structures on primary Hopf surfaces. We write out the developing map and holonomy morphism of each of these…

We investigate the minimal singularities of metrics on a big line bundle $L$ over a projective manifold when the stable base locus $Y$ of $L$ is a submanifold of codimension $r\geq 1$. Under some assumptions on the normal bundle and a…

We exhibit examples of slope-stable and modular vector bundles on a hyperk\"ahler manifold of K3$^{[2]}$-type which move in a 20-dimensional family and study their algebraic properties. These are obtained by performing standard linear…

Let D = {D_{1},...,D_{l}} be an arrangement of smooth hypersurfaces with normal crossings on the complex projective space P^n and let \Omega^{1}_{P^n}(log D) be the logarithmic bundle attached to it. Following [1], we show that…

We study line bundles on smooth toric DM stacks $\mathbb{P}_{\mathbf{\Sigma}}$ of arbitrary dimension. A sufficient condition is given for when infinitely many line bundles on $\mathbb{P}_{\mathbf{\Sigma}}$ have trivial cohomology. In…

We introduce logarithmic Picard algebroids, a natural class of Lie algebroids adapted to a simple normal crossings divisor on a smooth projective variety. We show that such algebroids are classified by a subspace of the de Rham cohomology…