On the Smooth Points of T-stable Varieties in G/B and the Peterson Map

2000/05/02 by James B. Carrell, Jochen Kuttler · 2 citations
Mathematics · #math.AG #msc:22F30

paper · pdf

published as Invent. Math. Online First November 8, 2002

arxiv created 2000/05/02 · arxiv updated 2009/11/30

Abstract

Let G be a semi-simple algebraic group over \mathbb C, B a Borel subgroup of G and T a maximal torus in B. A beautiful unpublished result of Dale Peterson says that if G is simply laced, then every rationally smooth point of a Schubert variety X in G/B is nonsingular in X. The purpose of this paper is to generalize this result to arbitrary T-stable subvarieties of G/B, the only restriction being that G contains no G₂ factors. In particular, we show that a Schubert variety X in such a G/B is nonsingular if and only if all the reduced tangent cones of X are linear.

Cited by

• Intersections of Schubert varieties and smooth T-stable subvarieties of flag varieties
• An anticanonical perspective on G/P Schubert varieties

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