In this paper we compute the cohomology of the Fano varieties of k-planes in the smooth complete intersection of two quadrics in P2g+1, using Springer theory for symmetric spaces.
Bibliographical noteFunding Information:
We thank the Max Planck Institute for Mathematics in Bonn for support, hospitality, and a nice research environment. Furthermore KV and TX thank the Research Institute for Mathematical Sciences in Kyoto for support, hospitality, and a nice research environment. Special thanks are due to Dennis Stanton for proving a key combinatorial identity and for writing an appendix containing the proof. We also thank the referee for the careful reading of the paper.
- Fano variety
- Hessenberg variety
- Hyperelliptic curve
- Springer correspondence
- Symmetric space