# Rationally smooth Schubert varieties and inversion hyperplane arrangements

@article{Slofstra2013RationallySS,
title={Rationally smooth Schubert varieties and inversion hyperplane arrangements},
author={William Slofstra},
year={2013},
volume={285},
pages={709-736}
}

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## References

SHOWING 1-10 OF 38 REFERENCES

• Mathematics
• 2010
We link Schubert varieties in the generalized flag manifolds with hyperplane arrangements. For an element of a Weyl group, we construct a certain graphical hyperplane arrangement. We show that the
• Mathematics
• 2014
A theorem of Ryan and Wolper states that a type A Schubert variety is smooth if and only if it is an iterated fibre bundle of Grassmannians. We extend this theorem to arbitrary finite type, showing
• Mathematics
• 2010
The purpose of this note is to give a refinement of the product formula proved in [1] for the Poincare polynomial of a smooth Schubert variety in the flag variety of an algebraic group G over C. This
We define an n-arrangement as a finite family of hyperplanes through the origin in C "+1. In [11] and [12] we studied the free arrangement and defined its structure sequence (their definitions will
• Mathematics
• 2002
Kazhdan-Lusztig polynomials Px,w(q) play an important role in the study of Schubert varieties as well as the representation theory of semisimple Lie algebras. We give a lower bound for the values
Although both the conjugacy classes and irreducible characters of all the individual Weyl groups have been determined, no unified approach has been obtained which makes use of the common structure of
We show that the hyperplane arrangement of a coconvex set in a finite root system is free if and only if it is free in corank 4. As a consequence, we show that the inversion arrangement of a Weyl