# Complete intersection hyperk\"{a}hler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one

@inproceedings{Lee2021CompleteIH, title={Complete intersection hyperk\"\{a\}hler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one}, author={Eunjeong Lee and Kyeong-Dong Park}, year={2021} }

We classify fourfolds with trivial canonical bundle which are zero loci of general global sections of completely reducible equivariant vector bundles over exceptional homogeneous varieties of Picard number one. As a result, we see that there exist no hyperkähler fourfolds among them. This completes similar classifications by Benedetti and Inoue–Ito–Miura for Grassmannians and isotropic (symplectic or orthogonal) Grassmannians.

## One Citation

### Topics on Fano varieties of K3 type

- Mathematics
- 2022

. This is a survey paper about a selection of recent results on the geometry of a special class of Fano varieties, which are called of K3 type. The focus is mostly Hodge-theoretical, with an eye…

## References

SHOWING 1-10 OF 24 REFERENCES

### Manifolds of low dimension with trivial canonical bundle in Grassmannians

- Mathematics
- 2016

We study fourfolds with trivial canonical bundle which are zero loci of sections of homogeneous, completely reducible bundles over ordinary and classical complex Grassmannians. We prove that the only…

### Complete intersection Calabi–Yau manifolds with respect to homogeneous vector bundles on Grassmannians

- MathematicsMathematische Zeitschrift
- 2018

Based on the method by Küchle (Math Z 218(4), 563–575, 1995), we give a procedure to list up all complete intersection Calabi–Yau manifolds with respect to direct sums of irreducible homogeneous…

### Calabi--Yau complete intersections in exceptional Grassmannians

- Mathematics
- 2016

. We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi–Yau 3-folds as complete intersections. We also calculate Hodge numbers for…

### On the derived category of the Cayley plane

- Mathematics
- 2009

We find a full strongly exceptional collection for the Cayley plane OP2, the simplest rational homogeneous space of the exceptional group E6. This collection, closely related to the one given by the…

### Hyper-Kähler fourfolds and Grassmann geometry

- Mathematics
- 2009

Abstract We construct a new 20-dimensional family of projective hyper-Kähler fourfolds and prove that they are deformation-equivalent to the second punctual Hilbert scheme of a K3 surface of genus 12.

### 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…

### Fano Varieties of K3-Type and IHS Manifolds

- Mathematics
- 2019

We construct several new families of Fano varieties of K3 type. We give a geometrical explanation of the K3 structure and we link some of them to projective families of irreducible holomorphic…

### On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*

- Mathematics
- 1978

Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent the…

### Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds

- Mathematics
- 2014

A bstractWe investigate the mathematical properties of the class of Calabi-Yau four-folds recently found in ref. [1]. This class consists of 921,497 configuration matrices which correspond to…

### On the projective geometry of rational homogeneous varieties

- Mathematics
- 1998

Abstract. We determine the varieties of linear spaces on rational homogeneous varieties, provide explicit geometric models for these spaces, and establish basic facts about the local differential…