Related papers: Non-existence of low rank Ulrich bundles on Verone…

Using structural properties of groups of small order, we establish the non-existence of varieties isogenous to a higher product of dimension $n$ greater than 3 with fixed topological Euler number $(-2)^n$ and trivial first Betti number.

We classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. In the process, we prove the stability of the sheaves of relative differentials on rational scrolls.

In the present paper we completely classify locally free sheaves of rank $2$ with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2\times\mathbb{P}^2\subseteq\mathbb{P}^8$ and its general hyperplane…

In this work we characterize Ulrich bundles of any rank on polarized rational ruled surfaces over $\mathbb{P}^1$. We show that every Ulrich bundle admits a resolution in terms of line bundles. Conversely, given an injective map between…

We prove that a double cover of $\mathbb{P}^2$ ramified along a general smooth curve B of degree $2s$, for $s \geq 3$, supports a rank 2 special Ulrich bundle.

Let $V$ be a $K$-vector space of dimension $n+1$. In this paper, we focus our attention into the existence of irreducible homogeneous Ulrich bundles on flag manifolds $\FF(p, q,n)$ which parameterizes all chains of linear subspaces $L_{p}…

Let $n\geq 4$, $2 \leq r \leq n-2$ and $e \geq 1$. We show that the intersection of the locus of degree $e$ morphisms from $\mathbb{P}^1$ to $G(r,n)$ with the restricted universal sub-bundles having a given splitting type and the locus of…

Let Gr(2, E) be the Grassmann bundle of two-planes associated to a general bundle E over a curve X. We prove that an embedding of Gr(2, E) by a certain twist of the relative Pl\"ucker map is not secant defective. This yields a new and more…

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our…

In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of…

We prove that for any $m\geq3$, $n\gg m^3$, all secant varieties of the Segre-Veronese variety $\mathbb{P}^m\times\mathbb{P}^n$ have the expected dimension. This was already proved by Abo and Brambilla in the subabundant case, hence we…

In this article, we give numerical restrictions on the Chern classes of Ulrich bundles on higher-dimensional manifolds, which are inspired by the results of Casnati in the case of surfaces. As a by-product, we prove that the only projective…

We describe the locus of stable bundles on a smooth genus $g$ curve that fail to be globally generated. For each rank $r$ and degree $d$ with $rg<d<r(2g-1)$, we exhibit a component of the expected dimension. We show moreover that no…

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…

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…

We show that any polarized K3 surface supports special Ulrich bundles of rank 2.

We prove existence of aCM and Ulrich sheaves respect to ample and globally generated polarisations on a class of special finite coverings $f:X\to\mathbb{P}^n$, which in particular contains cyclic ones. In the case of rank $2$ on double…

Let $L$ be a very ample line bundle on a projective scheme $X$ defined over an algebraically closed field $\Bbbk$ with ${\rm char}~\Bbbk \neq 2$. We say that $(X,L)$ satisfies property $\mathsf{QR}(k)$ if the homogeneous ideal of the…

This paper deals with syzygies of the ideals of the Veronese embeddings. We prove that O(3) on P^n satisfies Property N_4 for every n. Besides we prove that O(d) on P^n satisfies N_p for all n >= p iff O(d) on P^p satisfies N_p.

Let $SV^{\pmb n}_{\pmb d}$ be the Segre-Veronese given as the image of the embedding induced by the line bundle $\mathcal{O}_{\mathbb{P}^{n_1}\times\dots\times\mathbb{P}^{n_r}}(d_1,\dots, d_r)$. We prove that asymptotically $SV^{\pmb…