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The characteristic variety of a generic foliation

Jorge Vitório Pereira (2012)

Journal of the European Mathematical Society

We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

The Levi problem for cohomology classes

Mihnea Coltoiu (1984)

Annales de l'institut Fourier

In this paper we extend to complex spaces and coherent analytic sheaves some results of Andreotti and Norguet concerning the extension of cohomology classes.

The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, Alexander Schmeding (2015)

Studia Mathematica

We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense of Milnor. ...

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