## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Schubert Calculus — Osaka 2012, H. Naruse, T. Ikeda, M. Masuda and T. Tanisaki, eds. (Tokyo: Mathematical Society of Japan, 2016), 53 - 74

### Spherical multiple flags

Piotr Achinger and Nicolas Perrin

#### Abstract

For a reductive group $G$, the products of projective varieties homogeneous under $G$ that are spherical for the diagonal action of $G$ have been classified by Stembridge. We consider the $B$-orbit closures in these spherical varieties and prove that under some mild restrictions they are normal, Cohen-Macaulay and have a rational resolution.

#### Article information

**Dates**

Received: 27 July 2013

Revised: 20 July 2014

First available in Project Euclid:
4 October 2018

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1538622995

**Digital Object Identifier**

doi:10.2969/aspm/07110053

**Mathematical Reviews number (MathSciNet)**

MR3644819

**Zentralblatt MATH identifier**

1378.14049

**Subjects**

Primary: 14M27: Compactifications; symmetric and spherical varieties 20G15: Linear algebraic groups over arbitrary fields

**Keywords**

spherical varieties normal singularities rational resolutions homogeneous spaces

#### Citation

Achinger, Piotr; Perrin, Nicolas. Spherical multiple flags. Schubert Calculus — Osaka 2012, 53--74, Mathematical Society of Japan, Tokyo, Japan, 2016. doi:10.2969/aspm/07110053. https://projecteuclid.org/euclid.aspm/1538622995