Self-dual projective algebraic varieties associated with symmetric spaces

Details Self-dual projective algebraic varieties associated with symmetric spaces Self-dual projective algebraic varieties associated with symmetric spaces

2004-09-23

arxiv.org/abs/math/0409444v1

Algebraic Transformation Groups and Algebraic Varieties, Enc. Math. Sci., Vol. 132, Subseries Invariant Theory and Algebraic T

Mathematics

Analysis of PDEs

34 pages

Scientific paper

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 $X=\check X$ where $\check X$ is the projective dual of $X$. We give algebraic criteria of projective self-duality for the considered orbit closures.

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