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arXiv · 2002.05855

Poincare polynomials of generic torus orbit closures in Schubert varieties

Eunjeong Lee·Mikiya Masuda·Seonjeong Park·Jongbaek Song
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Abstract

The closure of a generic torus orbit in the flag variety $G/B$ of type $A$ is known to be a permutohedral variety and its Poincare polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincare polynomial of a generic torus orbit closure in a Schubert variety in $G/B$. When the generic torus orbit closure in a Schubert variety is smooth, its Poincare polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.

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Eunjeong Lee, Mikiya Masuda, Seonjeong Park, Jongbaek Song. 2020-02-14. Poincare polynomials of generic torus orbit closures in Schubert varieties. https://arxiv.org/abs/2002.05855

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