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Self-dual Projective Algebraic Varieties Associated With Symmetric Spaces

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Algebraic Transformation Groups and Algebraic Varieties

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 132))

Abstract

We discover a class of projective self-dual algebraic varieties. Namely, we consider actions of isotropy groups of complex symmetric spaces on the projectivized nilpotent varieties of isotropy modules. For them, we classify all orbit closures X such that \(X = \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} \) where \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} \) is the projective dual of X. We give algebraic criteria of projective self-duality for the considered orbit closures.

Partly supported by ESI, Vienna, Austria and ETH, Zürich, Switzerland.

Partly supported by ESI, Vienna, Austria.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, Moscow, 117966, Russia

    Vladimir L. Popov

  2. Department of Mathematics, The University of Texas, Austin, Texas, 78712, USA

    Evgueni A. Tevelev

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  1. Vladimir L. Popov
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  2. Evgueni A. Tevelev
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  1. Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 117966, Moscow, Russia

    Vladimir L. Popov

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Popov, V.L., Tevelev, E.A. (2004). Self-dual Projective Algebraic Varieties Associated With Symmetric Spaces. In: Popov, V.L. (eds) Algebraic Transformation Groups and Algebraic Varieties. Encyclopaedia of Mathematical Sciences, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05652-3_8

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  • DOI: https://doi.org/10.1007/978-3-662-05652-3_8

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