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We study the resolution of an Ulrich bundle of arbitrary rank on the Segre fourfold $PP^2timesPP^2$. We characterize the Ulrich bundles $Vv$ of arbitrary rank on $PP^2timesPP^2$ with $h^1(VvotimesOmegaboxtimesOmega)=0$ or with $h^1(VvotimesOmega(-1)boxtimesOmega(-1))=0$ or obtained as pullback from $PP^2$ and we construct more complicated examples.
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.
We show that any polarized K3 surface supports special Ulrich bundles of rank 2.
We assume that $mathcal{E}$ is a rank $r$ Ulrich bundle for $(P^n, mathcal{O}(d))$. The main result of this paper is that $mathcal{E}(i)otimes Omega^{j}(j)$ has natural cohomology for any integers $i in mathbb{Z}$ and $0 leq j leq n$, and every Ulric
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 of two Le
We study instanton bundles $E$ on $mathbb{P}^1times mathbb{P}^1 times mathbb{P}^1$. We construct two different monads which are the analog of the monads for instanton bundles on $mathbb P^3$ and on the flag threefold $F(0,1,2)$. We characterize the G