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On vector fields in C3 without a separatrix.

J. Olivares-Vázquez (1992)

Revista Matemática de la Universidad Complutense de Madrid

A family of germs at 0 of holomorphic vector fields in C3 without separatrices is constructed, with the aid of the blown-up foliation F in the blown-up manifold C3. We impose conditions on the multiplicity and the linear part of F at its singular points (i.e., non-semisimplicity and certain nonresonancy), which are sufficient for the original vector field to be separatrix-free.

Optimal destabilizing vectors in some Gauge theoretical moduli problems

Laurent Bruasse (2006)

Annales de l’institut Fourier

We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing 1 -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...

Properties of operators occurring in the Penrose transform

Zbyněk Šír (2001)

Commentationes Mathematicae Universitatis Carolinae

It is shown that operators occurring in the classical Penrose transform are differential. These operators are identified depending on line bundles over the twistor space.

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