TL;DR
This paper studies the geometric properties of B-orbit closures in spherical varieties associated with reductive groups, proving they are normal, Cohen-Macaulay, and admit rational resolutions under certain conditions.
Contribution
It extends the classification of spherical varieties by analyzing B-orbit closures and establishing their desirable geometric properties.
Findings
B-orbit closures are normal under mild restrictions
They are Cohen-Macaulay
They admit rational resolutions
Abstract
For a reductive group G, the products of projective rational varieties homogeneous under G that are spherical for 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.
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