English

On the Complex Cayley Grassmannian

Algebraic Geometry 2019-03-01 v2 Differential Geometry Representation Theory

Abstract

We define a torus action on the (complex) Cayley Grassmannian XX. Using this action, we prove that XX is a singular variety. We also show that the singular locus is smooth and has the same cohomology ring as that of CP5\mathbb{CP}^5. Furthermore, we identify the singular locus with a quotient of G2CG_2^\mathbb{C} by a parabolic subgroup.

Keywords

Cite

@article{arxiv.1711.05169,
  title  = {On the Complex Cayley Grassmannian},
  author = {Üstün Yıldırım},
  journal= {arXiv preprint arXiv:1711.05169},
  year   = {2019}
}

Comments

22 pages, 1 figure, naming convention changed, introduction rewritten, a discussion of the singular locus is added

R2 v1 2026-06-22T22:45:43.401Z