Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties

Details Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties

2001-03-05

arxiv.org/abs/math/0103022v1

Mathematics

Algebraic Geometry

20 pages, 2 figures

Scientific paper

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].

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