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Complex-symmetric spaces

Ralf Lehmann (1989)

Annales de l'institut Fourier

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 using...

Continuous Reinhardt domains from a Jordan viewpoint

L. L. Stachó (2008)

Studia Mathematica

As a natural extension of bounded complete Reinhardt domains in N to spaces of continuous functions, continuous Reinhardt domains (CRD) are bounded open connected solid sets in commutative C*-algebras with respect to the natural ordering. We give a complete parametric description for the structure of holomorphic isomorphisms between CRDs and characterize the partial Jordan triple structures which can be associated with some CRDs. On the basis of these results, we test two conjectures concerning...

Deformations of Kähler manifolds with nonvanishing holomorphic vector fields

Jaume Amorós, Mònica Manjarín, Marcel Nicolau (2012)

Journal of the European Mathematical Society

We study compact Kähler manifolds X admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of 𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛𝑠 , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of X . We extend Calabi’s theorem on the structure of compact Kähler...

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