# An introduction to Ulrich bundles

@article{Beauville2016AnIT, title={An introduction to Ulrich bundles}, author={Arnaud Beauville}, journal={European Journal of Mathematics}, year={2016}, volume={4}, pages={26-36} }

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

#### Paper Mentions

#### 51 Citations

On the existence of Ulrich vector bundles on some surfaces of maximal Albanese dimension

- Mathematics
- European Journal of Mathematics
- 2019

We establish the existence of simple Ulrich vector bundles on surfaces $$S \subset {\mathbb {P}}^N$$S⊂PN of maximal Albanese dimension with and .

Ulrich Trichotomy on del Pezzo surfaces.

- Mathematics
- 2020

In this article, we use a correspondence between Ulrich bundles on a projective variety and quiver representations to prove that certain del Pezzo surfaces satisfy the Ulrich trichotomy, for any… Expand

Ulrich and aCM bundles from invariant theory

- Mathematics
- Communications in Algebra
- 2019

Abstract We use certain special prehomogeneous representations of algebraic groups in order to construct aCM vector bundles, possibly Ulrich, on certain families of hypersurfaces. Among other… Expand

Examples of surfaces which are Ulrich–wild

- Mathematics
- 2018

We give examples of surfaces which are Ulrich-wild, i.e. that support families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.

On the existence of Ulrich vector bundles on some irregular surfaces

- Physics, Mathematics
- 2018

We establish the existence of rank two Ulrich vector bundles on surfaces that are either of maximal Albanese dimension or with irregularity 1, under many embeddings. In particular we get the first… Expand

Equivariant Ulrich bundles on exceptional homogeneous varieties

- Mathematics
- 2017

Abstract We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the Cayley plane… Expand

Ulrich Bundles on Three-Dimensional Scrolls

- Mathematics
- 2018

In this paper we construct Ulrich bundles of low rank on three-dimensional scrolls (with respect to the tautological line bundle). We pay special attention to the four types of threefold scrolls in… Expand

Iitaka dimension of vector bundles 1 2

- 2021

We present 25 open questions about moduli spaces of vector bundles and related topics, and discuss some longstanding conjectures. We hope to inspire young researchers to engage in this area of… Expand

Special Ulrich bundles on regular Weierstrass fibrations

- Mathematics
- Mathematische Zeitschrift
- 2019

The main goal of this short paper is to prove the existence of rank 2 simple and special Ulrich bundles on a wide class of elliptic surfaces: namely, on regular Weierstrass fibrations $$\pi :… Expand

Ulrich line bundles on double planes.

- Mathematics
- 2019

Consider a smooth complex surface $X$ which is a double cover of the projective plane $\mathbb{P}^2$ branched along a smooth curve of degree $2s$. In this article, we study the geometric conditions… Expand

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