Advanced Studies in Pure Mathematics

Spherical multiple flags

Piotr Achinger and Nicolas Perrin

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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

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

Received: 27 July 2013
Revised: 20 July 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document euclid.aspm/1538622995

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

spherical varieties normal singularities rational resolutions homogeneous spaces


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.

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