Classification of invariant AHS-structures on semisimple locally symmetric spaces

Jan Gregorovič

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A compact complex space $X$ is called complex-symmetric with respect to a subgroup $G$ of the group ${Aut}_{0} (X)$ , if each point of $X$ is isolated fixed point of an involutive automorphism of $G$ . It follows that $G$ is almost $G^{0}$ -homogeneous. After some examples we classify normal complex-symmetric varieties with $G^{0}$ reductive. It turns out that $X$ is a product of a Hermitian symmetric space and a compact torus embedding satisfying some additional conditions. In the smooth case these torus embeddings are classified...

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