English

Smoothness of Schubert varieties in twisted affine Grassmannians

Algebraic Geometry 2020-12-23 v4 Representation Theory

Abstract

We give a complete list of smooth and rationally smooth normalized Schubert varieties in the twisted affine Grassmannian associated with a tamely ramified group and a special vertex of its Bruhat-Tits building. The particular case of the quasi-minuscule Schubert variety in the quasi-split but non-split form of Spin8{\rm Spin}_8 ("ramified triality") provides an input needed in the article by He-Pappas-Rapoport classifying Shimura varieties with good or semi-stable reduction.

Keywords

Cite

@article{arxiv.1809.08464,
  title  = {Smoothness of Schubert varieties in twisted affine Grassmannians},
  author = {Thomas J. Haines and Timo Richarz},
  journal= {arXiv preprint arXiv:1809.08464},
  year   = {2020}
}

Comments

24 pages. Minor correction: certain lattices termed almost selfdual in the previous version are now correctly termed almost modular. The article has been recast to apply to normalized Schubert varieties, to account for the existence of non-normal Schubert varieties in small positive characteristics. A new Proposition 2.1 and a new proof of Proposition 2.2 have been given. Accepted version