Advanced Studies in Pure Mathematics

Spherical multiple flags

Piotr Achinger and Nicolas Perrin

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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

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

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


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