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Coleff-Herrera currents, duality, and noetherian operators

Mats Andersson (2011)

Bulletin de la Société Mathématique de France

Let be a coherent subsheaf of a locally free sheaf 𝒪 ( E 0 ) and suppose that = 𝒪 ( E 0 ) / has pure codimension. Starting with a residue current R obtained from a locally free resolution of we construct a vector-valued Coleff-Herrera current μ with support on the variety associated to such that φ is in if and only if μ φ = 0 . Such a current μ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction...

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...

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