# Irreducible Ulrich bundles on isotropic Grassmannians

@article{Fonarev2016IrreducibleUB, title={Irreducible Ulrich bundles on isotropic Grassmannians}, author={Anton Fonarev}, journal={arXiv: Algebraic Geometry}, year={2016} }

We classify irreducible equivariant Ulrich vector bundles on isotropic Grassmannians.

## 5 Citations

### Equivariant Ulrich bundles on exceptional homogeneous varieties

- MathematicsAdvances in Geometry
- 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…

### Homogeneous ACM bundles on exceptional isotropic Grassmannians

- Mathematics
- 2022

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles over exceptional isotropic Grassmannians in terms of their associated data. We show that there are only ﬁnitely…

### Arithmetically Cohen--Macaulay bundles on homogeneous varieties of Picard rank one

- Mathematics
- 2022

In this paper, we study arithmetically Cohen–Macaulay (ACM) bundles on homogeneous varieties G/P . Indeed we characterize the homogeneous ACM bundles on G/P of Picard rank one in terms of highest…

### Ulrich bundles on some twisted flags

- MathematicsRocky Mountain Journal of Mathematics
- 2020

In this note we prove that certain twisted flag varieties carry Ulrich bundles. Let X ⊂ P be a projective variety of dimension d. An Ulrich bundle on X is a vector bundle E satisfying H(X, E(−l)) = 0…

## 11 References

### $\GL(V)$-invariant Ulrich bundles on Grassmannians

- Mathematics
- 2014

In this paper, we give a full classification of all homogeneous Ulrich bundles on a Grassmannian $\Gr(k,n)$ of $k$-planes on $\PP^n$.

### Cohomology of Vector Bundles and Syzygies

- Mathematics
- 2003

1. Introduction 2. Schur functions and Schur complexes 3. Grassmannians and flag varieties 4. Bott's theorem 5. The geometric technique 6. The determinantal varieties 7. Higher rank varieties 8. The…

### On Küchle varieties with Picard number greater than 1

- Mathematics
- 2015

We describe the geometry of Küchle varieties (that is, Fano fourfolds of index 1 contained in Grassmannians as zero loci of sections of equivariant vector bundles) with Picard number greater than 1.…

### On the Kuznetsov-Polishchuk conjecture

- Mathematics
- 2015

We prove a conjecture by A. Kuznetsov and A. Polishchuk on the existence of some particular full exceptional collections in bounded derived categories of coherent sheaves on Grassmann varieties.

### Ulrich bundles on abelian surfaces

- Mathematics
- 2015

We prove that any abelian surface admits a rank 2 Ulrich bundle. Let X ⊂ P be a projective variety of dimension d over an algebraically closed field. An Ulrich bundle on X is a vector bundle E on X…

### Resultants and Chow forms via exterior syzygies

- Mathematics
- 2001

Let W be a vector space of dimension n+ 1 over a field K. The Chow divisor of a k-dimensional variety X in P = P(W ) is the hypersurface, in the Grassmannian Gk+1 of planes of codimension k+1 in P,…

### Homogeneous bundles”. In: Helices and vector bundles

- Vol. 148. London Math. Soc. Lec. Note Series
- 1990