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A cohomological Steinness criterion for holomorphically spreadable complex spaces

Viorel Vâjâitu (2010)

Czechoslovak Mathematical Journal

Let X be a complex space of dimension n , not necessarily reduced, whose cohomology groups H 1 ( X , 𝒪 ) , ... , H n - 1 ( X , 𝒪 ) are of finite dimension (as complex vector spaces). We show that X is Stein (resp., 1 -convex) if, and only if, X is holomorphically spreadable (resp., X is holomorphically spreadable at infinity). This, on the one hand, generalizes a known characterization of Stein spaces due to Siu, Laufer, and Simha and, on the other hand, it provides a new criterion for 1 -convexity.

Bounding the degree of solutions to Pfaff equations

Marco Brunella, Luis Gustavo Mendes (2000)

Publicacions Matemàtiques

We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.

Coleff-Herrera currents, duality, and noetherian operators

Mats Andersson (2011)

Bulletin de la Société Mathématique de France

Let ℐ be a coherent subsheaf of a locally free sheaf 𝒪 ( E 0 ) and suppose that ℱ = 𝒪 ( E 0 ) / ℐ has pure codimension. Starting with a residue current R obtained from a locally free resolution of ℱ we construct a vector-valued Coleff-Herrera current μ with support on the variety associated to ℱ such that φ is in ℐ 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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