Combinatorial Tangent Space and Rational Smoothness of Schubert\n Varieties

2001/03/05 by Stéphane Gaussent, Gaussent, Stéphane
Mathematics · #14M15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0103022

openalex publication_date 2001/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following Contou-Carrere [CC], we consider the Bott-Samelson resolution of a\nSchubert variety as a variety of galleries in the Tits building associated to\nthe situation. We prove that the rational smoothness of a Schubert variety can\nbe expressed in terms of a subspace of the Zariski tangent space called, the\ncombinatorial tangent space. For this, we use a characterization of rational\nsmoothness of a Schubert variety introduced by Carrell and Peterson [CP].\n

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