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NESTINGS OF RATIONAL HOMOGENEOUS VARIETIES

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Abstract

In this paper we study the existence of sections of universal bundles on rational homogeneous varieties–called nestings–classifying them completely on rational homogeneous varieties G/P in the case where G is a simple group of classical type and P is a parabolic subgroup of G. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of the automorphism group acting transitively on the base variety.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, Calle Tulipán, 28933, Móstoles, Madrid, Spain

    ROBERTO MUÑOZ

  2. Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38123, Trento, (TN), Italy

    GIANLUCA OCCHETTA & LUIS E. SOLÁ CONDE

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  1. ROBERTO MUÑOZ
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  2. GIANLUCA OCCHETTA
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  3. LUIS E. SOLÁ CONDE
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Correspondence to ROBERTO MUÑOZ.

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ROBERTO MUÑOZ is Supported by MTM2015-65968-P.

GIANLUCA OCCHETTA is Supported by PRIN project “Geometria delle varietà algebriche”, by the Miur-FFABR 2017 project, and by the Department of Mathematics of the University of Trento.

LUIS E. SOLÁ CONDE is Supported by PRIN project “Geometria delle varietà algebriche”, by the Miur-FFABR 2017 project, and by the Department of Mathematics of the University of Trento. Partially supported by the Polish National Science Center project 2013/08/A/ST1/00804.

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MUÑOZ, R., OCCHETTA, G. & SOLÁ CONDE, L.E. NESTINGS OF RATIONAL HOMOGENEOUS VARIETIES. Transformation Groups 27, 189–223 (2022). https://doi.org/10.1007/s00031-020-09597-x

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