Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties
Algebraic Geometry
2016-09-07 v1
Abstract
Following Contou-Carrere [CC], we consider the Bott-Samelson resolution of a Schubert variety as a variety of galleries in the Tits building associated to the situation. We prove that the rational smoothness of a Schubert variety can be expressed in terms of a subspace of the Zariski tangent space called, the combinatorial tangent space. For this, we use a characterization of rational smoothness of a Schubert variety introduced by Carrell and Peterson [CP].
Cite
@article{arxiv.math/0103022,
title = {Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties},
author = {Stéphane Gaussent},
journal= {arXiv preprint arXiv:math/0103022},
year = {2016}
}
Comments
20 pages, 2 figures