Related papers: Linear and Steiner bundles on projective varieties

We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by…

In this paper we construct indecomposable vector bundles associated to monads on Cartesian products of odd dimension projective spaces. Specifically we establish the existence of monads on…

In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.

We prove a Horrocks-type splitting criterion for arbitrary smooth projective toric varieties under an additional hypothesis similar to the case of products of projective spaces by Eisenbud--Erman--Schreyer.

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

We introduce multi-uniformized stacks as a generalization of the Abramovich--Hassett construction of uniformized twisted varieties. We prove an equivalence between the category of multi $\mathbb{Q}$-line bundles satisfying an analogue of…

We equate dynamical properties (e.g., positive entropy, existence of a periodic curve) of complex projective surface automorphisms with properties of the pull-back actions of such automorphisms on line bundles. We use the properties of the…

We define the isomorphism classes of torus-equivariant rank 2 arithmetically Cohen-Macaulay (aCM) vector bundles on the Veronese surface, up to a twist by the hyperplane class, and count them. Our approach makes use of Klyachko's…

We provide unipotent factorizations of vector bundle automorphisms of real and complex vector bundles over smooth manifolds. This generalises work of Thurston-Wasserstein and Wasserstein for trivial vector bundles. We also address two…

There is a standard method to calculate the cohomology of torus-invariant sheaves $L$ on a toric variety via the simplicial cohomology of associated subsets $V(L)$ of the space $N_{\mathbb R}$ of 1-parameter subgroups of the torus. For a…

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

We define a notion of morphism for quotient vector bundles that yields both a category $\textit{QVBun}$ and a contravariant global sections functor $C:\textit{QVBun}^{\textrm{op}}\to\textit{Vect}$ whose restriction to trivial vector bundles…

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method…

We confirm Beauville's conjecture that claims that if the p-th exterior power of the tangent bundle of a smooth projective variety contains the p-th power of an ample line bundle, then the variety is either the projective space or the…

We use certain special prehomogeneous representations of algebraic groups in order to construct aCM vector bundles, possibly Ulrich, on certain families of hypersurfaces. Among other results, we show that a general cubic hypersurface of…

In this review, novel non-standard techniques for the computation of cohomology classes on toric varieties are summarized. After an introduction of the basic definitions and properties of toric geometry, we discuss a specific computational…

In this paper we give top most and least indices of non vanishing cohomology modules of line bundles in the Kac Moody setting in terms of Weyl group combinatorics. We also prove a surjection Theorem.

The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra being a Hopf-Galois extension. A…

We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with…

We study the linearization of line bundles and the local structure of actions of connected linear algebraic groups, in the setting of seminormal varieties. We show that several classical results about normal varieties extend to that…