Related papers: Equivariant Ulrich bundles on flag varieties

We define a variety of doubly indexed flags, this is a smooth, projective variety, and we describe it as an iterated over Grassmannian varieties. On the other hand, we consider the variety of partial flags which are stabilized by a given…

In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of $\mathbb{P}^{3}$, $Q$ (smooth quadric in $\mathbb{P}^{4}$), $V_{3}$ (smooth cubic in…

Let X be a smooth projective variety carrying an Ulrich bundle. In the first part of this note, we construct an Ulrich sheaf on n-th symmetric power of X, which is a singular variety when $DimX >1$. As a consequence, we get the existence of…

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.

We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E appears as an extension…

We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2\le d\leq n-d)$ to be the Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where…

We give a classification of rank $r$ torus equivariant vector bundles $\mathcal{E}$ on a toric scheme $\mathfrak{X}$ over a discrete valuation ring $\mathcal{O}$, in terms of graded piecewise linear maps $\Phi$ from the fan of…

We generalize the results by Eisenbud and Schreyer about Ulrich bundles over Veronese varieties to Segre-Veronese varieties. We discuss the range where we have natural cohomology and we construct multigraded resolutions and monads for…

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 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…

This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type A. The quiver flag variety M_\vartheta(Q,r) of a finite acyclic quiver Q (with a unique source) and a…

I prove that a vector bundle on a minuscule homogeneous variety splits into a direct sum of line bundles if and only if its restriction to the union of two-dimensional Schubert subvarieties splits. A case-by-case analysis is done.

We prove that the modular component $\mathcal M(r)$, constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank $r$ and given Chern classes,…

If $X\subset\operatorname{Gr}(2,6)$ is the Fano variety of lines of a smooth cubic fourfold, then we show that the restriction to $X$ of any Schur functor of the tautological quotient bundle is modular and slope polystable. Moreover it is…

We classify holomorphic as well as algebraic torus equivariant principal $G$-bundles over a nonsingular toric variety $X$, where $G$ is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric…

This article lays the foundations for the study of modular forms transforming with respect to representations of Fuchsian groups of genus zero. More precisely, we define geometrically weighted graded modules of such modular forms, where the…

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of…

We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.

We give a permutation pattern avoidance criteria for determining when the projection map from the flag variety to a Grassmannian induces a fiber bundle structure on a Schubert variety. In particular, we introduce the notion of a split…

We prove that any surface with q=p_g=0 embedded by a sufficiently large linear system admits a rank 2 Ulrich bundle. In particular every Enriques surface admits a rank 2 Ulrich bundle.