Related papers: Uniform Steiner bundles on $\mathbb{P}^n$ and refl…

Let $\mathbb{k}$ be an algebraically closed field. Connections between representations of the generalized Kronecker quivers $K_r$ and vector bundles on $\mathbb{P}^{r-1}$ have been known for quite some time. This article is concerned with a…

In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible…

There is a long-standing conjecture which states that every uniform algebraic vector bundle of rank $r<2n$ on the $n$-dimensional projective space $\mathbb{P}^n$ over an algebraically closed field of characteristic $0$ is homogeneous. This…

The Hilbert scheme of n points in the projective plane parameterizes degree n zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying…

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an…

We study the principal parts bundles $P^k (L)$ of the degree $d$ line bundle $L$ on the $n$ dimensional projective space as homogeneous bundles and we describe their associated quiver representations. We use this approach to show that if…

Let $n$, $k$, and $t$ be integers satisfying $n>k>t\ge2$. A Steiner system with parameters $t$, $k$, and $n$ is a $k$-uniform hypergraph on $n$ vertices in which every set of $t$ distinct vertices is contained in exactly one edge. An…

We define Schwarzenberger bundles on any smooth projective variety X. We introduce the notions of jumping pairs of a Steiner bundle E on X and determine a bound for the dimension of its jumping locus. We completely classify Steiner bundles…

A Steiner bundle is a vector bundle on projective space arising as the cokernel of the map defined by a matrix of linear forms. These come up in various geometric settings, and by now they are the subject of a considerable literature.…

In order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such…

We prove existence and unicity of slope stable vector bundles on a general polarized hyperk\"ahler (HK) variety of type $K3^{[n]}$ with certain discrete invariants, provided the rank and the first two Chern classes of the vector bundle…

We find lower bounds on the rank of a "real" vector bundle over an involutive space, such that "real" vector bundles of higher rank have a trivial summand and such that a stable isomorphism for such bundles implies ordinary isomorphism. We…

In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an…

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of…

We define symmetric bundles as vector bundles in the category of symmetric spaces; it is shown that this notion is the geometric analog of the one of a representation of a Lie triple system. We show that such a bundle has an underlying…

We partially extend to hyperk\"ahler fourfolds of Kummer type the results that we have proved regarding stable rigid vector bundles on hyperk\"ahler (HK) varieties of type $K3^{[n]}$. Let $(M,h)$ be a general polarized HK fourfold of Kummer…

Nested Steiner quadruple systems are designs derived from Steiner quadruple systems (SQSs) by partitioning each block into pairs. A nested SQS is completely uniform if every possible pair appears with equal multiplicity, and completely…

We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is…

Over a scheme with 2 invertible, we show that a vector bundle of rank four has a sub or quotient line bundle if and only if the canonical symmetric bilinear form on its exterior square has a lagrangian subspace. For this, we exploit a…

Let $X$ be a K3 surface. We prove that Addington's $\mathbb{P}^n$-functor between the derived categories of $X$ and the Hilbert scheme of points $X^{[k]}$ maps stable vector bundles on $X$ to stable vector bundles on $X^{[k]}$, given some…