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Minimal rational curves on generalized Bott–Samelson varieties

Part of: Linear algebraic groups and related topics Algebraic groups Special varieties Cycles and subschemes

Published online by Cambridge University Press:  15 February 2021

Michel Brion  and
S. Senthamarai Kannan
Michel Brion
Affiliation:
Université Grenoble Alpes, 100 rue des Mathématiques, 38610Gières, FranceMichel.Brion@univ-grenoble-alpes.fr
S. Senthamarai Kannan
Affiliation:
Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam603103, Indiakannan@cmi.ac.in
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Abstract

We investigate families of minimal rational curves on Schubert varieties, their Bott–Samelson desingularizations, and their generalizations constructed by Nicolas Perrin in the minuscule case. In particular, we describe the minimal families on small resolutions of minuscule Schubert varieties.

Keywords

minimal rational curveSchubert varietyBott–Samelson variety

MSC classification

Primary: 14C05: Parametrization (Chow and Hilbert schemes) 14M15: Grassmannians, Schubert varieties, flag manifolds
Secondary: 14L30: Group actions on varieties or schemes (quotients) 20G05: Representation theory
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 1 , January 2021 , pp. 122 - 153
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Copyright
© The Author(s) 2021

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Footnotes

To the memory of C. S. Seshadri

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