Related papers: Ulrich bundles on cubic fourfolds

In this short note, we study the existence problem for Ulrich bundles on ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient $\alpha$ of…

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…

We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class of the even Clifford algebra…

We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold not containing a plane in terms of moduli spaces. We show that the blow-up $Z'$ along the cubic of the irreducible holomorphic symplectic…

We characterize smooth irreducible varieties with Ulrich twisted normal bundle.

In this note, which is an addendum to the e-print math.AG/9810121, we prove that the variety VSP(F,10) of presentations of a general cubic form F in 6 variables as a sum of 10 cubes is a smooth symplectic 4-fold, which is deformation…

We derive a formula for the unramified Brauer group of a general class of rationally connected fourfolds birational to conic bundles over smooth threefolds. We produce new examples of conic bundles over P^3 where this formula applies and…

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…

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,…

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…

Given an orthogonal bundle $E$ over a smooth projective curve $X$ we define a Hecke transformation in the moduli space of orthogonal bundles by performing an elementary transformation with respect to a Lagrangian submodule $L \subset…

In this paper, we compute an explicit matrix factorization of a rank 9 Ulrich sheaf on a general cubic hypersurface of dimension at most 7, whose existence was proved by Manivel. Instead of using invariant theory, we use Shamash's…

Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspondence between representations of the generalized…

We study rank 2 $h$-instanton sheaves on projective threefolds. We demonstrate that any orientable rank 2, non-locally free $h$-instanton sheaf with defect 0 on a threefold can be obtained as an elementary transformation of a locally free…

We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $\leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. We apply…

Let $S$ be a surface with $p_g(S)=0$, $q(S)=1$ and endowed with a very ample line bundle $\mathcal O_S(h)$ such that $h^1\big(S,\mathcal O_S(h)\big)=0$. We show that such an $S$ supports families of dimension $p$ of pairwise non-isomorphic,…

In this paper we address a conjecture by Kleppe and Mir\'o-Roig stating that suitable twists by line bundles (on the smooth locus) of the exterior powers of the normal sheaf of a standard determinantal locus are arithmetically…

We define special objects, Ulrich objects, on a derived category of polarized smooth projective variety as a generalization of Ulrich bundles to the derived category. These are defined by the cohomological conditions that are the same form…

We show that a smooth projective non-degenerate arithmetically Cohen-Macaulay subvariety X of P^N infinite Cohen-Macaulay type becomes of finite Cohen-Macaulay type by removing Ulrich bundles if and only if N = 5 and X is a quartic scroll…

Given a smooth non-hyperelliptic prime Fano threefold X, we prove the existence of all rank 2 ACM vector bundles on X by deformation of semistable sheaves. We show that these bundles move in generically smooth components of the…