相关论文: Positivity of Ulrich bundles in the ample and free…

We characterize $q$-ample Ulrich bundles on a variety $X \subseteq \mathbb P^N$ with respect to $(q+1)$-dimensional linear spaces contained in $X$.

We study the positivity of the first Chern class of a rank r Ulrich vector bundle E on a smooth n-dimensional variety $X \subseteq \mathbb P^N$. We prove that $c_1(E)$ is very positive on every subvariety not contained in the union of lines…

In this paper we prove a generalization of a theorem of Schneider, which gives a criterion for a projective surface over the complex numbers to have an ample cotangent bundle. After reviewing different notions of positivity, we introduce a…

In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb…

After recalling the definition and basic properties of Ulrich bundles, we focus on the existence problem: does any smooth projective variety carry a Ulrich bundle? We show that the Serre construction provides a positive answer on certain…

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 on $X_n$, the plane blown--up at $n$ general points, there are Ulrich line bundles with respect to a line bundle corresponding to curves of degree $m$ passing simply through the $n$ blown--up points, with $m\leq 2\sqrt{n}$ and…

Given a projective variety $X$ and a very ample line bundle $\mathcal{L}$ on $X$, we classify for which $X$ and $\mathcal{L}$ the twisted syzygies and twisted dual syzygies bundles are Ulrich with respect to the polarizations…

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,…

Let $X$ be a smooth projective variety of dimension $n$, and let $E$ be an ample vector bundle over $X$. We show that any non-zero Schur class of $E$, lying in the cohomology group of bidegree $(n-1, n-1)$, has a representative which is…

Let $X$ be the blow up of $\mathbb{P}^2$ at $r$ general points $p_1,\ldots,p_r \in \mathbb{P}^2$. We study line bundles on $X$ given by plane curves of degree $d$ passing through $p_i$ with multiplicity $m_i$. We establish conditions for…

We investigate various positivity properties of line bundles on general blow ups of Hirzebruch surfaces motivated by \cite{Han}, where the author has studied general blow ups of $\mathbb{P}^2$. For each of the properties: ampleness, global…

We study geometrical properties of an Ulrich vector bundle $E$ of rank $r$ on a smooth $n$-dimensional variety $X \subseteq \mathbb P^N$. We characterize ampleness of $E$ and of $\det E$ in terms of the restriction to lines contained in…

The aim of this note is to shed some light on the relationships among some notions of positivity for vector bundles that arose in recent decades. Our purpose is to study several of the positivity notions studied for vector bundles with some…

We construct an Ulrich bundle on the blowup at a point when the original variety is embedded by a sufficiently positive linear system and carries an Ulrich bundle. In particular, we describe the relation between special Ulrich bundles on…

In this article, we prove that any smooth projective variety $X$ which is a double cover of the projective space $\mathbb{P}^n$ ($n\geq 2$) admits an Ulrich bundle. When $n=2$, we show that on any such $X$, there is an Ulrich bundle of rank…

Fixed a polarised variety $X$, we can ask if it admits Ulrich bundles and, in case, what is their minimal possible rank. In this thesis, after recalling general properties of Ulrich sheaves, we show that any finite covering of…

Let $E$ be a vector bundle and $S_a$, $S_b$ the Schur functors associated to partitions $a$ and $b$. Previously we have shown that ampleness of $S_aE$ implies ampleness of $S_bE$ when $a$ is greater than $b$ in the dominance partial order.…

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 investigate the existence of Ulrich vector bundles on suitable $3$-fold scrolls $X_e$ over Hirzebruch surfaces $\mathbb{F}_e$, for any integer $e \geqslant 0$, which arise as tautological embeddings of projectivization of very-ample…